One of the first things you learn when racing in the rain is that the dry line is likely not the fastest/grippiest line in the wet. That's because the dry line tends to have a lot of rubber laid down on it, and this rubber layer can be slick when wet. The dry line can also be polished smooth over time, whereas the less used part of the pavement tends to be more abrasive and porous, making for better grip in the wet. It's also important to be aware of the fact that paint and concrete tend to have a lot less grip when wet (because these surfaces are less porous), so it's best to avoid concrete patches or painted lines or curbs.
Every track is different in the rain because the age and condition of its asphalt varies and drainage tends to differ too. So it always takes some experimentation to find the grippiest/fastest line around a circuit in the wet, but as a general rule it's best to shorten the turns and lengthen the straights by going in deeper, making a sharper but slower turn and then using a very late apex. And since water runs downhill, if a corner is banked you'll probably find more grip (less water) up high in the turn. Point being, use your eyes and your head and you'll find the driest and grippiest parts of the track to use when racing in the rain.
Now that you have an idea of how your tires will behave in the wet and how to find the best wet line, it's time to consider how your car behaves in the wet and how you as a driver can best control it. Traction changes in the wet, but not necessarily in a predictable way. Braking isn't nearly as compromised as acceleration. This means the driver will find himself struggling more with controlling wheelspin coming out of corners than fighting brake lock-up. It's also important to be conscious of the fact that lateral grip (cornering) is reduced more in the rain than longitudinal grip (braking and acceleration), so even though you may feel like there's great grip under braking don't be fooled into thinking the same amount of grip will be available in the turns or when jumping on the gas pedal.
Because lateral grip is so compromised in the wet, cornering speeds will be lower and weight transfer will be reduced, resulting in less body roll. This means that your car doesn't need as much roll resistance in the wet, allowing you to run your shock settings and sway bar settings at full soft (assuming your car is equipped with adjustable dampers and bars). Pro race teams even go so far as swapping softer springs onto the car if rain is a certainty. Softer suspension settings will allow the tires to stay in more constant and consistent contact with the road, and that's key to maximizing what little grip is available on a wet surface. Softer suspension settings will also make the car more forgiving to drive.
If you race a FWD or AWD vehicle that tends to understeer a fair bit in the dry, you may be accustomed to trail braking (braking while initiating turn-in for a corner) to induce some rotation. However, trail braking in the rain is a big no-no. In the rain, it's always best to brake, turn and accelerate in a deliberate and separate fashion - combine any of these and the result often includes a backward trip through the weeds.
Similarly, in the dry you may be accustomed to using short quick applications of the throttle to adjust the car's attitude in the turns and then jumping on the gas aggressively once you've got the car more or less pointed in the direction of the next straight. In the wet a subtler technique is required, where only smooth and gradual applications of the go pedal will avoid wheelspin and speed-robbing understeer.
Perhaps the biggest challenge when racing in the rain is visibility. Your helmet visor and windscreen can fog up and wheel spray from the cars in front of you can put up a wall of mist that is virtually impossible to see through. Hopefully, your car has a blower motor or windscreen defogger, but if it doesn't then applying some defogger solution (spraying on and wiping off foam shaving cream works remarkably well as a ghetto solution) to both sides of the windscreen and your helmet's visor is a good start. Rain-X is also a great product that helps speed rain drops off your windscreen, so much so that you won't even need to run your windshield wipers unless the rain is absolutely torrential.
As far as avoiding spray from other cars goes, the best solution is to be out front. If you follow the tips included in this story and get out there and practice, practice, practice in the rain, chances are you'll be out front kicking up lots of spray for the poor buggers behind you. Keeping your driving smooth, minimize tire slip angle, find the grippiest parts of the track and you'll also be the first to see checkered flag.
The Real Rainman
Jackie Stewart may not be able to count how many toothpicks hit the ground if you dropped a box of them on the floor, but he's undoubtedly one of the greatest rain racing drivers of all time. Under a thick fog and heavy rain, Sir Jackie dominated the '68 F1 German Grand Prix at the Nürburgring Nordschleife and a formidable lineup of racing legends including Jackie Ickx, Graham Hill and John Surtees. Starting sixth on the grid and nursing a broken wrist, Stewart knew he'd have no chance if he got caught in the blinding spray behind the lead cars, so on the first lap he charged to the front and never looked back, finishing the race some 4 minutes, 3 seconds ahead of the second-place finisher.