not sue if this is the right place for this. Haven't been around the forums long enough to know. here's what I know:
Experience is gained by walking, flying and driving vehicles and ships. you can also gain XP for paying faction salaries, prospecting,mining (?) and producing (?).
You can apply to join a faction under the manage section in your inventory. They accept you or reject you after that.
Verdre To already gave you a nice overview. I also suggest you read The Guide, take a look at the rules pages and check out the websites of those factions you are interested in.