What exactly is FRC?

I know what it stands for, but I just want to know what kind of competitions there are (please be specific).

well, to start, there are 37 (i believe) regional events that are internationally spread out, with team lists ranging from 35 to 70 teams competing. on the first day of competition (out of three) every team gets about 3 or 4 practice matches to test their robots. also, every robot needs to get inspected to make sure it is legal and it abides by the rules. Then, on the second day, the real competition begins. each team has 6 or 7 qualifying matches, which rank them into the competition standings. one the third day, the final matches begin to see who will win the competition. the top eight teams form the eight alliances of three robots each, each alliance picks two other teams to help them win. then it is just like a tournament ladder, where the #1 team plays against the #8 team. for an alliance to advance, they must win two out of three matches.

thats basically what happens at the regionals that i have gone to, but maybe the smaller ones differ.

how is the game played?

It varies from year to year… At the Kick Off, they tell you what the Game will be… The Kick Off for VEX, it was in SEP-2006, for FRC, it was JAN-2007.