Aliens Colonial Marines

In addition to Oh Jay Arr's comment, you can also gain XP by playing online. As you can imagine, ranking up to level 2 is very quick, and it unlocked for me after my first game of escape (I think level 2 is 1000XP).

Will be one of the very first achievements you unlock, either in SP or MP.

All progress through the campaign and by attempting challenges will increase your XP level. You should get your first promotion quite easily during the first mission, especially if (like I was) you're playing on Ultimate Badass difficulty and keeping an eye on your challenges. I don't know the exact amount of XP required for Rank 2 but I do know that a meter in the top right-hand corner of the screen tracks your progress towards the next level-up.