You've presumably "found" a solution by now, given the amount of time that has passed, but for anyone else curious, experience is principally gained through ground combat (if you chose the Dauntless startup then you should certainly have acquired enough experience to gain some levels).

Characters that are eligible for a level increase will have a green plus shown on the bottom right of their character icon - if you select them and then go to the character screen, you should have 5 points available to add to their existing characteristics (or a multiple of 5 if you have several levels' worth of progress).

To add to what AstralWanderer mentioned, you gain exp in skills as well. Every time you say, fire a weapon or hack something, you gain exp and when you have enough, that skill levels up. So you get stats from leveling up your characters and your character's skill dynamically levels up as you use them.

Not sure how much more RPG you can get...heh.