Just to elaborate on the Avanti description a bit:
Like TF2 maps, you have the attackers/defenders and a setup time at the start of the game. The defenders start at the final capture point at the top of the map, while the attackers start with a flag in their "spawn" way downhill.
Once the gates are open, the attackers must take their flag a short distance to the first capture point. If they suceed in doing this, the point is captured and the flag removed. After a little while, the flag is spawned on that capture point. The attackers must then take that flag to the next capture point further uphill.
If the flag carrier is killed, the flag will drop to the ground. If it is left without getting picked up for a while, it will return to the the last point that was captured (spawn if no point has yet been taken).
Once the third point has been captured, victory is declared and the teams swap. Then the whole thing starts over again.
One of the nice things about Avanti was the map layout. Becuase the attackers start way downhill and must reach the church at the top, you always know where you're going. Just head upwards. There's always this constant "uphill struggle" thing going on.