Reaching level 60 goes pretty fast since progress towards your ranks can be earned through all game modes. One great method for earning XP (aside from completing challenges) is to play a 2 vs. 2 Extermination private match. (Note: host will always be an alien for the 1st round) When you're a marine, each of you take a waypoint to stand in a circle to destroy eggs. Destroy as many as you can before time runs out. By the end of the round, you'll easily have over 1,000 XP earned. As an alien, just chill.
Experience is earned from kills, collectables, completing challenges, match bonuses and campaign chapters completed. Assists are unconfirmed.
Mission 11 (Home) is a great way to rank up too. Complete this mission on Ultimate Baddass for around 2,800 XP. This level is incredibly easy with 2 people, one occupying the queen and the other presses the first 4 buttons. Meet up behind the last button, wait for the queen to get on the path and BAM! Let her have it.