Start by unplugging it and begin to carefully take it apart.
Start from the back using a phillips screwdriver, and you may need to buy a *security* torque driver to remove one of the screws in the back. (a *security* torque driver is the 6 sided star shaped driver with a hole in the middle, the hole is the *security* part of it)
Identify the spider. Is it dead? It could be dangerous, if it is a brown recluse or black widow.
The microwave still works? Ok, great. How long did you leave it in storage in the garage or whatever, for it to get a spider in it? Was it cleaned before it was stored?
You need to take this microwave apart and carefully note how each piece fits into the next (write it down, draw yourself pictures or something), because one spider in view could mean a whole lot more going on elsewhere inside that microwave. Gross.
Or just learn to not question the hidden mysteries in your microwave, and accept that spider just as a reminder not to cook Halloween candy in the microwave in that wax looking paper that actually is foil paper on the other side.
As far as worrying about gross things going on inside your microwave, don't, that was just a joke.
Besides I'm sure that they are all cooked by now! ;)
Ewwwh!, October 2009