Exercise caution when working around electronics and unless you are well versed in automotive electronics DO NOT USE A TEST LIGHT. Although many times it is harmless to use a test light, in only takes one poke to destroy a 5 thousand dollar body controller.
In the dash is the Cadillac car stereo and tape deck.
Wire connections tools
GM antenna adapter (prior to about 88 you will not need this)
Crimp caps or electrical tape
Look along the woodgrain trim piece around the radio for two bolts along the upper edge, if they are there remove them, if not just remove the trim. Remove the Cadillac car stereo.
Remove the metal sleeve from the aftermarket radio with enclosed keys. Assemble the dash kit according to the dash kit instructions for the model year. You will need the dash kit piece which offsets the radio 1.5 or so inches beyond the point at which the old radio sat and it will stick out a bit. Insert the ring into the dash kit assembly and bend back the appropriate metal tabs.
Connect aftermarket Cadillac car stereo harness and wiring harness wires verbatim. Connect the bare ends together. Black to black, red to red and so on. There may be some that are not used such as orange with black etc. Tape those connections off. Don't forget the blue wire or the power antenna will not go up.
Plug in the harness to the aftermarket radio along with the antenna adapter and the dash harness and clip radio in to the metal sleeve. Install the Cadillac car stereo into the opening and reinstall the trim ring.