DISCLAIMER: Follow these at your own risk. I'm not responsible for you damaging your car/injuring yourself/harming anything or anyone else. You shouldn't be touching suspension unless you have a good idea what you're doing.
I just got done installing coilovers and figured I'd share some of the things I picked up on while doing it. I went by this DIY for MkIV coilovers...they are almost identical up front (minus the swaybar links) and the rears are very similar to a FWD TT. http://www.nclh.org/car/coilover_howto/
Keep in mind, I have a FWD which is different in the rear...however even the quattro doesn't look that different.
Tip #1: Use air tools.
If you don't have air tools find someone who does. A lot of nuts in the suspension are nylon locknuts and an incredible pain to remove by hand. This way you also won't need special tools to remove nuts from the strut towers.
Tip #2: Make sure you have a spindle spreader tool and proper spring compressor.
You have to pry the front spindles apart to remove the front struts; there is a special tool for this. It's just a little socket tool with an oval shaped bit that's used to pry the spindle apart. It's available on ECSTuning for about $25 if I recall.
Also, if you rent spring compressors from AutoZone ($50 when you rent them, you get the $50 back when you return them) make sure you ask for STRUT SPRING COMPRESSORS. Initially I rented a pair of "spring compressors" and they were not the correct parts. You need "strut compressors" or "strut spring compressors" even though most people and DIYs just call them "spring compressors."
Tip #3: Replace your front strut bushings/bearings.
Not only is this good for refreshing your suspension, it also saves you from needing to take apart your OEM struts to retreive the bushings/bearings.
Tip #4: Use loctite blue.
Suspension components are constantly exposed to vibration and force...you don't want the bolts working themselves loose. Get a tube of loctite blue and put it on all the bolts you install...a lot of the nuts are locknuts but I still used loctite anyway.
Tip #5: Removing the front struts.
The front driver's side comes right out. You can get the control arm plenty low enough to just take the strut right out and put the new one right in.
However the passenger's side, for whatever reason, does not go down anywhere near as low. This makes it a bit of a pain to get the strut out.
At first I tried to compress the spring far enough to get some clearance to remove the strut....I hit the damn thing with four spring compressors and it still wouldn't come out. Point behind using more than two was that compressing several of the coils would give me access to the other coils then I'd compress those with the other pair...but this still wasn't working. I was doing this at a friend's garage and he didn't have a socket to remove the upper strut nut (deep 21mm)...so I couldn't get the bushing out. If I could have gotten the bushing out I MAY have had enough clearance to remove it.
There is BARELY ANY clearance to even get spring compressors in there...even the spring coils themselves are hard to get the spring compressors onto. Here's what I'm talking about:
What I ended up doing was disonnecting the tie rod from the spindle and removing the ball joints. This allowed me to move the spindle enough to get the strut out. Here's a pic of it removed...notice how I had four spring compressors on it by this point:
I'm not sure if spring compressors would have been necessary to remove it this way, I'm going to guess that they wouldn't have.
Make sure you put the ball joints back where they were or at least both in the same position. They are usually the whole way to the inside of the control arm. They should pretty much sit themselves in this position when you go to reassemble anyway. If you move them it adjusts your camber.
The part of the tie rod end that bolts into the spindle doesn't have any adjustment, so you shouldn't throw off your toe just by removing it. You'll need an alignment for the rears anyhow if you're quattro so you might as well get an alignement for good measure.
Tip #6: Removing rear springs.
Since my car is FWD, its rear suspension is a torsion beam setup. The torsion beam is pretty robust, however the quattro fully independent suspension might not be so robust.
That said the way I removed the rear springs on my FWD involved two people. I jacked up one corner, put it on stands and removed the wheel (obviously) then had my buddy stand on the rear brake caliper while I snatched the rear spring out. Again this might not be a good idea with rear control arms in the quattro (or in general) but it worked for me. Worst comes to worst you would just use a spring compressor to compress the spring and then remove it. However using my method you can have the spring out in notime.
Tip #7: Removing rear shock mounts.
You'll notice if you just try and unscrew the shock mount off the shock the shock will just spin. Have a vice grip or a pair of channel locks and a rag (to not damage the old/new one) ready to clamp down the shock so you can remove the nut that holds the mount.