I was actually fixing the iPhone of a friend of mine. The silver part of the mute switch of his phone had broken off, and he had to use a sharpened pencil to mute and unmute the phone.
Surprisingly well! I was a little intimidated by the "difficult"-label this guide has on iFixit (esp. as this was my very first phone-DIY-experience), but things went very smoothly. Didn't take too long either (45 minutes or so).
1. the iFixit-guide mentions using a #00 screwdriver, but I found a #000 to be handier.
2. I found it to be unnecessary to take the volume button circuitry and headphone jack assembly completely out of the phone as steps 21-23 suggest: as soon as the volume button circuitry is loose, you can lift it just enough to take out the old mute switch and replace it with the new one.
3. Replacing the motherboard in exactly the right position is without question the trickiest part of this entire (dis)assembly!