How do I become a 'Good Sport' and what rewards can I receive?
You'll become a "bad sport" by leaving missions/races/deatchmatches etc. early and destroying other player's personal vehicles.
The "bad sport" designation lasts for about 2 days. So if you want to be a "good sport" again, don't do things that are considered bad for 2 days.
I am not 100% sure what you can get as a reward. I once got a cash bonus of 1000$, but there could be more things (like discounts on ingame items).
Source: IGN