When the air conditioner "freezes up," it's meant quite literally. There is ice on anything not insulated; consequently, the flow of cool air is almost completely stopped.
This can be caused if there is a dirty air filter preventing the free flow of cold air, meaning the air conditioning unit will run more than it needs to. Change the air filter.
If this doesn't help, turn off the air conditioner for several hours and allow the ice to melt. It's possible the air conditioner was simply running for too long at one time.
If the air conditioner works fine after restarting it, be more mindful of how long you let the device run. If the unit freezes up again almost immediately, there's likely a slow leak of coolant, in which case a professional should be called to diagnose and remedy the problem.
Will Not Run
First determine whether the entire unit won't run or just the compressor. If the fan works, but won't blow cold air, then it's the compressor.
If the fan won't run either, then it's an electrical fault and should be seen to immediately by a professional to avoid the possibility of a fire hazard. If the compressor won't run, remove the compressor terminal cover near the front of the device.
It's likely that one or two of the compressor terminal wires have overheated and lost contact with the leads connecting them to the compressor. New compressor terminals can be obtained from a well-stocked hardware store.
Replacing them takes a few minutes' work stripping the wires and connecting the new ones.
Outdoor Compressor Will Not Turn Off
The outdoor compressor will not shut off when there is something wrong with the contactor terminals running from the compressor to the indoor unit. In many cases, insects can get caught between the leads of the contactor.
They die, but their bodies still cause electricity to flow through the leads, preventing the compressor from shutting off when it should. Disconnect the power going through the system and look at your contactor, near the back of the compressor.
You may be able to remove the leads, clean the contactor and get it running again, but if the leads are charred black, then the heat buildup from the constantly running compressor has already damaged the component, and the contactor should be replaced.