A lot of the things I mention may seem obvious, but judging from my online experience they are not!!!

1. Be cool and try to give space to others at the start of the race. Avoid aggressive moves at the first corner. Most accidents happen there. Don't forget that your tires are still cold!
2. If you have high ping (above 200), be extra careful or even consider disconnecting. Others will see your car teleporting around and it will be very difficult to race bumper to bumper.
3. Always use the virtual mirror (F11).
4. Use the map application so you can see where the other cars are.
5. If you hit someone by accident, wait for him and give his position back when it is safe to do so.
6. If you get out of the track, be extra careful when rejoining it. Be sure that noone is coming when you rejoin or come out of the pits. Rejoin the track parallel to the track edge, not perpendicular.
7. When you are getting lapped by the first racers, just stay where you are. Don't try to change your line, because that's not what is expected. You are expected to hold your line and just let the first drivers pass.
8. If you run in a multiclass server, be careful at the braking points. Other cars may brake earlier/later than yours.
9. Don't divebomb. For example if you are more than one care length behind the car in front, don't dive into the corner. Just wait for the right opportunity for a clean pass.
10. Don't use other cars as brakes :D
11. If you see smoke or wreckage in front, go slower. If you try to pass at full speed, there is a high probability that you'll wreck too!
12. Be predictable.

Respect your opponents and have clean and nice races!

Game footage taken from Assetto Corsa version 0.20.5.