The objective in sprints is to minimise your lap time. It doesn't matter which run results in your best time(s). In sprints you have the luxury of being able to experiment - if something you try doesn't work, it doesn't matter; just change the plan next lap.
For most people, times will improve during the day before flattening out or even worsening later in the day. This is a natural and normal pattern even for very experienced drivers. Every time you sprint, the conditions are slightly different, even if your car is supposedly the same:
It is only natural that it take a few runs to optimise your performance given these differences. The optimisation process, unless your are still relatively inexperienced, should only be a matter of fine-tweaking rather than wholesale change. For inexperienced drivers, drivers in a new car, or drivers at a track for the first time, these changes are overwhelmed by the process of finding the best line, gear selection, and braking points.
If you can, practice with an experienced racing driver critiqueing your lines, braking points, cornerspeed etc. This is probably the quickest and easiest way to get a rapid improvement in your times. The friendly expert could be a passenger (if allowed), or could be following behind you on the track or even observing from the sidelines. In either case, they will have an excellent view of what you are doing right and wrong. You should also take the opportunity to follow behind more experienced drivers and observe their driving. Unless you are improving very rapidly or they are in a much slower car, you may not be able to keep up for long :-)
A small minority of people somehow manage to do their best times on the first run. I suspect this may be due to these drivers artificially making the task of improving too complex - that is they distract themselves down by thinking too much. Another likely reason is that later in the day they are trying too hard, and in the process slowing themselves down.
Given all that, there are a lot of different variables that can be adjusted from run to run.
The simplest adjustment is tyre pressure. You don't need any special facilities and unless your car has significant handling problems, they are all you will need to change. If your car has adjustable anti-roll bars, adjustable (telescopic) dampers, or adjustable suspension geometry, you have additional degrees of freedom which are probably best determined by a seperate testing day (the skid pan at Winton looks good for this).
The first thing to consider about tyre pressures is that you should not be running street settings on the track. A reasonable starting point for most cars/tyres is 40 psi all round. You can adjust each end of the car more or less independently based on wear, tread temperature and the car's handling characteristics.
You should probably set upper and lower constraints on tyre pressures so that you don't go too crazy on adjustments. 34psi to 46psi is probably reasonable for most cars/tyres.
The most accurate method is to use a tyre pyrometer to measure rubber temperature across the width of the tyre. Most people don't have a pyrometer so we'll skip to the budget methods.
Some of the newer high performance tyres (like the BFG 230 R1) are designed to be more tolerant of camber changes, so it might be worth experimenting with tyres if you can't (or won't) change the suspension setup
Finally, once you have found a good tyre setup, check the actual tyre temperature just before you go out to your next run and bleed off any excess pressure. Unless there is a long gap between runs, the pressure will be higher since the heat from disk brakes and from the tyre casing will raise the temperature and therefore pressure of the air inside the tyre.
This is the most important way of improving your times. Even with the best car in class, you could still be 10 secs off the pace. If your were paying for a 10 second improvement by car modifications, you'd be up for many a pretty penny!
Before we discuss specific improvements, remember one thing. Sprints are a personal challenge between you and the clock. You should not feel under pressure to pass someone, to beat someone else's time, or set a personal best every time you head out in the car. The best way to enjoy your motorsport is to drive within the limits of your driving and your car. That way you won't end up in hospital and/or with an expensive wreck. In other words, don't go faster than you feel comfortable with at this stage - be prepared to learn as slowly as it takes.
Before you start, make sure that your driving position is comfortable, that the mirrors are adjusted and you know how to use them :-)
One good driving position is to place the seat such that with you back pressed into the seat and your arms outstretched in front of you, that your wrists rest on the top of the steering wheel. When you put your hands into the 10-2 position, you be the correct distance to confortably manage hand-over-hand steering.
Of course, make sure your restraint is on tight and your helmet is done up tight!!!
You should decide exactly how you want to drive around the circuit.
If this is your first time at a circuit, then it is really helpful to draw a top view of the track on a large piece of paper. A3 sheets are excellent, a portable whiteboard even better! Draw the track in pencil and when you have got it all to scale (including track width), draw over it with a felt tip pen (not if you are using the whiteboard!) so that, back with the pencil, you can scribble erasible notes and lines over your diagram.
Before you even head out onto the track, you should be able to make a passible attempt at the best lines around the circuit. The basic considerations that affect the lines you choose are:
The initial plan (before you drive onto the circuit) can be pretty sparse. It will only include your attempt at planning the best line.
During the first practice session (you only get one practice session for MSCA sprints), you should travel around at a relatively slow pace (i.e. no more than 80-90% of your limit) and try and follow your planned line. At each braking area, look for recognizable features you can use later for optimising your braking points.
Take note of any "special features" of the track that are on your planned line. This should include bumps, off-camber road profile, ripple strips or painted sections, changes in surface. Each of these things may cause a line change, may artificially limit your speed through that section or may act as braking markers and the like.
This is a good time to figure out what the right gear is for each corner. As a novice, err on the side of a higher gear (i.e. choose 3rd over 2nd if you aren't sure) - that way you won't overrev the engine as you pick up speed.
Finally consider your steering inputs as you follow the planned line. The most common mistake is to apex too early. Fortunately it is easy to pick up. If you need to add more steering (i.e. turn the wheel into the corner) anytime after you have apexed the corner, you have apexed too early. Ideally you should be continually unwinding the steering after the apex. This allows you to improve your corner exit speed (getting on the throttle early) which will always give you better times. So turn in a bit later and therefore open up the corner exit.
Note that in a series of turns (i.e. esses), the critical apex is the last apex. To get the final apex right, you have to have to take very lates apexes on the previous corner(s) in the esses.
If you do get more than one practice session, come off now and mark line changes and everything else you noted onto your map.
Before you head out again, re-examine the map, mentally drive the circuit over and over, perform mental experiments on lines were the right line may not be obvious etc. Make sure you know gear change points, and braking points as well as your lines.
You now have a plan which you can review and modify with experience.
After each run, review your laps and determine where you failed to follow the plan accurately. You may have failed to correctly execute your plan by missing an apex, locking up your brakes, backing off the throttle after apex, etc etc. If you know your plan well enough, any failures to follow the plan will be easily recognisable events that you should remember!
When you can repeatably adhere to the plan, you can move onto the next step -- improving the plan.
The second most common error is to enter a corner too quickly (i.e. too late on the brakes or trying to corner at too high a speed). You'll hear this over and over again. You will likely ignore the advice over and over again, but I'll try anyway: You'll get your fastest times by increasing corner exit speed - Slow In Fast Out.
If you are slithering around at the start of the corner, you've blown it. Slow Down! Get off the brakes early, on the power early and try to smoothly accelerate all the way through the corner. Later on you can get into advanced techniques like trail braking and deliberately inducing lift throttle oversteer, but for now keep it simple and smooth.You will get your biggest and easiest improvements this way.
The next biggest improvement is braking. The first point to note is that you will stop much faster if you don't use your engine to brake. Under heavy braking, disengage the clutch completely. From 60km/hr, I stop about 1.5m (5ft) shorter by using this technique. Unless your brakes have overheated, most modern cars can easily lock up their tyres.
The next point to note is that you shouldn't lock up your brakes. You'll take longer to slow down and you'll ruin expensive tyres. The best braking is threshold braking. That is the tyres are about to lock-up, but haven't yet. It will take practice to consistently threshold brake, but you will develop a feel for holding it on the limit if you practice enough. You will find it easier if you use the ball of your foot or even your toes to apply pressure to the pedal. Try and pivot around your ankle instead of "stepping" onto the pedal - it gives your more finesse.
Another common error is to apply too much throttle at the exit of slow corners. Try to maximise throttle while avoiding any wheelspin. You will accelerate faster and you won't unnecessarily destroy expensive tyres.
The final major step to improving your plan is to increase cornering speed on sweepers. Just as most inexperienced drivers push too hard in slow corners, they don't push hard enough in fast corners. Providing you don't get off line, you can make big improvements in laps times by finding your limit on the big sweepers. Don't be afraid to have the car in a 4 wheel drift - it still grips and steers well enough, but at the same time keep throttle and steering inputs smooth and gentle. The surest way to spin on a big sweeper is coarse throttle inputs.
Once you have mastered the art of making and optimising your plan and you feel you have reached a plateau, you can look at some additional driver techniques.
Left-foot Braking is exactly what you'd suspect -- using your left foot on the brake pedal instead of your right foot. It is useful primarily to eliminate the time delay between braking before a corner and applying throttle in the corner. This means you can brake slightly later and apply throttle earlier with the resultant earlier (potential) acceleration. Earlier throttle also will give you smoother cornering more control. Also, good left foot braking provides a smoother transition between braking and acceleration thus unsettling the car less.
Left foot braking is also useful when you just need a "dab" on the brakes to (say) settle the car, slow the car slightly, or check the you actually still have brakes!
If you haven't used left foot braking before, be prepared to learn finesse braking all over again. I know that at first, my left foot was a binary operator!
Trail Braking is braking while turning. Trail braking is used to minimize understeer (push) or cause oversteer (looseness). It is particularly useful in cars with natural understeer, especially front wheel drive cars.
The reason that trail braking works is that a tyre will generate more cornering force if there is increased weight on the wheel and will generate less cornering force if there is decreased weight on the wheel. Applying the brakes causes a weight transfer from the rear of the car to the front of the car and therefore increases cornering power at the front and reduces it at the rear of the car.
One of the golden rules of driving fast is to make your inputs (steering, throttle, brakes etc) as smooth as possible. You can improve the smoothness of downchanges (i.e. from 3rd gear to second gear) by matching the engine RPM as you engage the clutch. Phil Ethier's article on double clutching explains this very well, but a brief explanation is in order. At a given road speed in say 2nd gear, the engine RPM will be higher than they would be in 3rd gear. Conversely, if you are changing from 3rd gear to 2nd gear, the engine RPM must increase. If you allow the gearbox synchros and clutch to do this for you, you will transmit a fairly large braking force to the driving wheels. Given that you are already threshold braking, this sudden additional braking force will cause a lockup of the driving wheels. In a front wheel drive car you will understeer off the line (you have less grip when the tyres are locked up) while in a rear wheel drive car you will possibly spin the car. Neither case is desirable and is avoidable by increasing the engine RPM appropriately before the clutch is engaged. If you get it right, there will be no acceleration or deceleration forces transmitted to the driving wheels.
The following scenario allows you to brake, change down smoothly and efficiently:
You will find it difficult to match revs exactly without a lot of practice, Furthermore, you will find it very difficult to apply uniform braking pressure while you blip the throttle. Be patient, with (a lot of) practice you can overcome these problems.
Once you become a really tricky driver, you can use clutchless shifts, left foot braking and RPM matching and forget all you learnt about left foot braking. This is not recommended for most drivers and certainly not until you are very very good at RPM matching.