Most of the time, you're trying to solve different types of locks: key locks, 3 and 4 digit combination locks, combination locks with letters, directional locks (not going to say always try the Konami code, but there's a good chance that's going to be the answer), stuff like that. You may have to solve riddles to figure out where the keys and combinations are.
Some puzzles are purely observation. The Jurassic Park "hide stuff in the bottom of a Barbasol can" trick is pretty popular, there are safes where they tell you the code is the "boss's wife's birthday", so you have to find the calendar or rolodex or dated happy birthday note in the room.
There was one room I did that swapped the keycaps on a typewriter to make a substitution cipher- type the coded message into the typewriter and the decoded message would come out.
The rooms with higher production quality tend to incorporate more technology into the puzzles. One room I did gave you instructions on a radio (which you got from a previous locked box), if you were tuned to the right station- hinted at from a different clue, with the radio instructions changing as you finished each step. Another room had rigged together a large box with a Kinect or Leap Motion or something similar setup where you had to stick your hand into the box and move it around in the right place to open a magnetic lock, but the screen showing you the correct sequence was in another room that you couldn't see so your teammates had to be in the other room shouting directions at you.