Here's the exchange between the bunch of drunks staggering out of the pub in Act 2, scene 3:
Toby. ……. Shall wee rowze the night-Owle in a Catch, that will drawe three soules out of one Weauer? Shall we do that?
Andrew Aguecheek: And you loue me, let's doo't: I am dogge at a Catch.
Clown. Byrlady sir, and some dogs will catch well.
An. Most certaine: Let our Catch be, Thou Knaue.
Clown. Hold thy peace, thou Knaue knight. I shall be constrain'd in't, to call thee knaue, Knight.
Andrew Aguecheek. 'Tis not the first time I haue constrained one to call me knaue. Begin foole: it begins, Hold thy peace.
Clown. I shall neuer begin if I hold my peace.
An. Good ifaith: Come begin.
There's enough phrases in there that are also in a round published by Thomas Ravenscroft in 1609 that we can guess that that's the one used. (Scroll down the previous entry to see the music they sang from) Considering they weren't drunk the class did an admirable job of singing the round. (Or maybe they were.)
As for 'Come away death' there's nothing surviving so you just have to find a tune that the words fit (hard to do as the text has a very charactaristic number of syllables) or make up a tune yourself.