The first step would be to immerse yourself in as many grunge bands and songs as you can. Like, do nothing but listen to grunge music for several weeks. Meantime, find as much info you can on what equipment those specific bands are using. Look up the lyrics and see what kind of subjects they write about.
Basically, in order to play grunge you have to know what it is, what it's history is and where it comes from.
There's a whole bunch of sites around that go into the history of certain types of music...where it first started, who the first bands were etc...
I'd buy their music and also look around on usenet for early bootleg copies of live recordings or outtakes from the studio.

I did that for the Beatles. I'd heard all their officially released songs but found out that all the early takes and alternate versions were available as well. So I went out and bought a book that outlined the studio dates and what songs were recorded, looked at pictures of their studio and where the mics were placed, then spent months studying how the recordings were made and mixed down from 4 track, what instruments they used, what changes were made to the songs in order to improve them.
Kinda treat it like a university course in music and learn as much as you can.