What is the best quick repair for a drain pipe?
Depending on how and where it broke it going to affect what you can use.  I'm going to assume you're not looking for a suggestion of duct tape.

For long straight sections, where I had to cut a pipe, I've used rubber pipe connectors.  You just slip it on one side of the break, align the pipes, and slip it over the break and tighten down the hose clamps.

There also exist pipe wraps that harden to do temporary repairs, that you can find in most hardware stores, but I've never used it.

I've used epoxy putty when I had a leak right at a coupling, so I wasn't able to get wrap something tightly right where it was.  You just knead it together, press it into the leak, and wait for it to set up.