This is one of Slash's best solos. Performing it whilst dancing on top of a grand piano is not necessary. Though it does make you look cool. Let's break it down...
As with most Gn'R the tuning is Low Eb:Ab:Db:Gb:Bb:Eb. We've slowed things down a lot. This means the faster parts will be much easier to follow.
C5 Powerchord intro - This is the intro to the outro, if you get what we mean. Slash joins in with Izzy in building up to the solo by belting out the C5 powerchord. Yup. We're still in the Key of C for this song.
Main Phrase - After the outro has kicked off (and pianos are being danced on) Slash begins with the main phrase. The main phrase begins here and ends here.
A main phrase is a lick that defines the rest of the solo. It's the catchy part that everybody hums, and is repeated a lot. After each time the main phrase is played, Slash then diverges into something fiddly.
The main phrase itself is pretty easy and cool to play. Just be careful about the bends. The first bend is usually a half bend (bend up by 1 note, not 2 notes). On occasion he drops back a fret and then does a full bend - like here. You can cheat and just play the regular phrase. No-one will notice.
So after the first main phrase, comes the first fiddly part. It will take practice to get fast, just get it right slowly first, then build your speed. Little licks like this are often the most work in this type of solo.
So, then we have the next appearance of the main phrase. Exactly the same as the first time. And it is also followed by another fiddly part. This is the trickiest part of the solo, and no-one will look at you harshly for skipping it or dumbing it down to play an easier lick. That said, if you are determined and methodical, you will crack it. Get it right at a slow pace, it doesn't matter how slow as long as you get it right. Then start building speed. Your fingers will know where to go with enough practice, and you'll be surprised how fast you can get them to go if you work hard at it.
Main phrase 3 - Love this part. Here Slash plays the main phrase again, but starts a fret lower and does a full bend. Also he does this lovely blues bend, closely followed by the next fiddly bit (which is much easier than the others so far).
The rest of the solo is just more of the same. Remember the format:
main phrase followed by a fiddly bit until the end of the song.
Main phrase 4 - Fiddly bit
Main phrase 4 - Fiddly bit
Main phrase 4 - Fiddly bit
After that, take a bow and call the piano repairman.