I was just given payday the heist last night and several of my buddies are already in the 30s. Is there a good way I could catch up fast?
If you have a low level, you can play the first level (the bank) in hard mode, solo or coop. The level is easy enough to achieve and you can easily farm the challenges (X frags with weapon Y, etc) by camping nearby the iron gateway or above the safe room.
In general, the easiest way to quickly level up is to achieve the challenges offered by the game. You can find a list of these in the main menu. Some of them will only unlock when you'll have finished others, so you might discover new challenges to accomplish later.