Problem scenario
You want to remove a car stereo. Can something go wrong if so what should you look out for?
Solution
Yes. The airbags could be triggered. The car alarm could go off. Some anti-theft devices sound an alarm if the car stereo is tampered with.
You do not want the airbags to potentially inflate suddenly causing injury to you. They may have a capacitor or way of inflating without the car battery; be careful. The Supplemental Restraint System (which controls and includes airbags), aka SRS, should be disabled before working near the SRS components or wiring (per page 12-23 of the Haynes Repair Manual for the Toyota Corolla and Geo/Chevrolet Prizm 1993 thru 2002). For a Geo Prizm or Toyota Corolla 1993 through 2002, you can disconnect the battery for two minutes and put the key in and turn to "LOCK" to disable the airbag. Other makes and models of vehicles may have different methods for disabling the airbags.
The car alarm may have its own battery. If you disconnect the main battery and something is tampered with, the car alarm could start going off.
Screws could fall into the chassis or the area behind the stereo. (Sometimes there are screws if there is a mounting bracket. This can be common in smaller cars.)
You may want to buy a battery-powered headlamp (as the car battery may be unplugged or there may be insufficient light in the areas you need to see).
You will likely need two "keys" (that can come in an automotive radio removal kit). Car radio keys are not that expensive. What could work are two strips of plumber's straps (or Simpson Strong ties) or flathead screw drivers to insert on the left and righthand sides of the radio when you are facing it. This will make the radio release.
To remove the plastic panels inside (to fully access the radio as it may enclose the radio on the perimeter), you may need a flat head screwdriver.
Generally, not that many things go wrong. You can have limited knowledge of cars, and it will not be that difficult. You want to be careful of the things mentioned above (and possibly other things if your car has customization).