It really depends on the style and model. If you can tell me that, I can give you a better answer.
Ours had 2 lag bolts that went through the cabinet or shelf that is right above it and then into the top of the microwave. You loosen those while the 2nd person holds the front of the microwave. The back is sitting on a tab that is attached to the wall, so you basically tilt the front down and lift the back off the tabs.
I've read of others that have a release mechanism that you have to unlock. That's why I asked for the model number and brand.