Go to
http://www.allegacademy.org/ and read the Cadet I stuff if you want to be useful to the team. There's a (mostly forum) program called Cadet that guides new players and you can ask any questions in there.
Its also recommended not to spend much time on the newbie servers or you could pick wrong habits.
Game is usually played on conquest:
-Team who destroys or caps all of the enemy's tech bases wins
Tech bases: Garrison, Tactical Lab., Supremacy Center. Expansion Complex. (Some factions have other special tech bases but this are the common ones)
As a new player, useful things you can do:
Defend miners. (They get you money for buying more tech)
Kill enemy miners.
Probe (so you can see inbound enemy bombers or other threats)
There is a Teamspeak channel (ts.alleg.net), there is usually some people there who can help you with questions. Or simply ask your doubts in the lobby.
-Kap