The fuses for an air conditioner are similar to those in your home, your car and many electronic devices. They protect the air conditioner from excessive current. If too much electricity surges through the AC unit, a fuse will blow and the unit will shut off. You can check these air conditioner fuses by taking a look at the compartment on the unit where the fuses are stored.
Open your air conditioner's fuse box and look for a blown fuse (in the case of an in-wall unit). If a fuse is blown, the small electrical conductor on the inside of the fuse will be split in half instead of appearing solid. This will typically be a compartment located somewhere on the case of the air conditioner itself. The original manual for your air conditioner will have a diagram of all its parts. Use this diagram to find the fuse box on your specific model.
Go to the main fuse box in your home (if you have fuses instead of circuit breakers) and verify that the problem with your air conditioner isn't with this box as opposed to the standalone AC unit itself. Open the home fuse box and turn the main power switch to "off" to cut power to the box. Examine the fuse that is connected to the electrical circuit powering your air conditioning. Look at the top to see if the element on the inside is burned or melted. If it is, the fuse will need to be replaced before you can use your air conditioner again. If you have central air conditioning, the unit itself will likely not have its own fuse built in -- you will have to check your home fuse box.
Turn your car's engine off. Open the fuse box, which is typically located on or under your dashboard. The user's manual that came with your car will have a fuse diagram, indicating which fuse is powering your car's air conditioning system. Remove the fuse with your finger (or with the included metal or plastic clamping device) and examine the end to see if the element inside the fuse is broken, melted or burned. If it is, the fuse will need to be replaced.