What tools are required to unclog sink drain with garbage disposal?
Have a look at the trap under your sink. Assuming it's PVC with large plastic nuts, all you should need is ChannelLock pliers:



Unscrew the trap from the wall and disposal, and clean the trap itself, or snake the drain going into the wall, depending on where your clog is. Be sure to have a bucket and towels handy since there will be water backed up before the clog and in the trap.

If you can't find the clog either in the trap or with the snake, and you know it's further down the drain (try running some water through the disposal and into the bucket with the trap out), then I have family that swear by these drain bladders that attach to a garden hose, get inserted into the drain (past the vent) and they swell up to seal your end of the pipe while sending water down until the clog is forced out:



Each one of these will cost around $20 give or take, well less than a visit from a plumber.