Vortex has really helped me with my 2003 Jetta brakes, so I thought I would add something I couldn't find. I'm a nOOb so I hope this helps someone out there.
As all the posts say, if you have a BLACK Coolant Temp Sensor, it WILL fail. This was a 1.5 hour job, so it was worth the time. NEVER NEVER perform this maintenance while the engine is hot. Coolant WILL leak and can cause severe burns. I waited overnight and did mine in the morning. I also removed my negative battery terminal just in case.
1) I went to the stealership and bought the following parts:
Green Coolant Temperature Sensor (CTS) (part #: 059 919 501A) = $27
O-Ring = $1.25
2X Clips (I didn't break mine, but people have) = $.75
Total w. Tax = $30

2) I had some extra paint, so I highlighted the CTS cap with it. It's a tight squeeze!

3) This is just a zoomed in view so you can see how the clip is oriented. There are two of them, one for the CTS and the one to the outside of that.

4) I couldn't fit my hands in there, so I removed a couple brackets that were in the way. (allen wrench and 10mm wrench)

5) With a little bit more room now, I could get a LONG flat head under the CTS clip. A gentle upward pull worked for mine.

6) All I had was a regular set of 8" pliers. A LONG needle-nose would have been better. Just wiggle and pull.

7) The other posts said there would be some coolant leaking, but I didn't expect the volume that bled from the line!

8) Once the leaking stopped, I removed the old CTS and had to pull the o-ring from inside the housing.

9) Put the new o-ring on the GREEN sensor, and slide it back into the hose.

10) Slide the clip back in, put the wire harness back on the sensor, and re-attach the brackets.

When finished, I added about 3/4 of a gallon of coolant (mix of 50% coolant / 50% water). One bottle cost me $15. It was the pink stuff so it's more expensive. Part of the reason I took the neg. battery terminal off was to allow the computer to reset and recognize the new sensor. I have read others had problems with check engine lights (CEL).
My next project is a new Autotech.com exhaust kit!