I've been to four escape rooms. They had very different themes, puzzles, and difficulty levels. In one we were "locked" (you're never actually locked in at any I've been to) in two jail cells that had a tube connecting them, and we had to work together with the other cell to decipher the half-clues each cell had been given. Only by working together could we escape. In another we were in the office of an international spy, trying to figure out where they had disappeared to. In another we were in the study of a detective.
The goal of these places is to attract all different kinds of customers, so they have all different kinds of puzzles. There are often word games, tactile things like turning knobs a certain way, balls in actual mazes, number problems, cryptic messages to decode, etc. There are often padlocks on several objects around the room, with your goal being to figure out the combination.
Sometimes they give you clues, sometimes you have to ask for them, sometimes there is a screen with a countdown timer and information, sometimes it's someone talking to you over a speaker. It really varies!
The most important thing about any escape room is who you bring with you. Being with the right people can make it a fun and easy-going experience. Being with people you don't know very well can make it awkward, and being with family can lead to tension.