If you just want to tie one on and forget about it, a safe length of 18" or 24" will work in a lot of situations, but it should vary depending on where in the water column the fish are feeding, how deep the water is and what type of fly you are dropping. Most of the time, you'll probably want the nymph to be bouncing just along the bottom of the stream. Whenever you do tie on a dropper though, add more tippet than the depth you want to drop, as the dropper will usually be drifting behind the fly you're dropping from, not hanging straight down. Current will also affect how much or how little extra tippet you'll want to tie. Until you get used to casting a 2 or 3 fly rig, you'll want to check them frequently to make sure you haven't gotten them tangled...
"I wish I was fishin'..." -me