This is really far too broad, but this is a long journey to be starting on, so let me throw you a bone - from where you can go off & do some more research of your own.
Kurt Cobain mainly used Fenders on Nevermind - Mustang, Jaguar & Strat. The Strat had humbuckers retrofitted. The Mustang & Jaguar are unspecified, so we don't know whether it used simple single coil or P90s. He owned both at the time.
He used a Mesa-Boogie Studio head, Crown amp & Marshall 4x12. Also on the album was a Vox AC 30 & a Fender Bassman. Other than the Bassman [Lithium], we don't know which amp was used on which tracks.
Pedals were a Boss DS-1 distortion & Electro-Harmonix Small Clone chorus - which is what you hear on Come as You Are.
So, what does that boil down to?
A lot of money.
I'm a big fan of modelling amps, which usually come with a slew of effects pedal sound-alikes too. The basic distortion & chorus in most of these tend to be based on those two pedals, so they come 'free' with another 10 or so amps… including MesaBoogie , Vox AC30 etc.
I use an old Line6 UX2 which is guitar/mic amp, FX pedals & computer interface all in one. It took me about 4 minutes to copy the Come as You Are sound. I used a Telecaster* with the tone rolled off [it sounds like his guitar strings are pretty old & I've just changed mine] The chorus is such a significant part of the sound that I found it didn't really matter what amp I put it through, I could get close enough on a Vox, Marshall & MesaBoogie (though I had to back the Boogie off a long way, it's too hot otherwise). I could get pretty close with a Strat too - again the chorus pedal does most of the heavy lifting.
He plays his guitar tuned down to D, which I didn't bother with for this test, I just transposed.
A friend of mine uses a more modern equivalent of my Line6, a Yamaha THR II. You can now edit these things from your phone. Mine needs the computer. Apart from that, they're the same kind of thing. Multiple amps & pedals, dial in what you need. USB to computer. Some even come with a free DAW to get you started on recording.
These days it's really easy to Google what gear someone used on a record. Once you figure it out, you just dial in the same amp & pedals on your modelling amp. All you need to be able to do then is figure out exactly how they played it.
Info predominantly sourced from GuitarWorld - The definitive Kurt Cobain gear guide
* I also use a modelling guitar, so I've got literally 50 guitars to choose from