1. Field strip the gun so you have the side with the recoil spring and barrel removed.
2. Set the slide on your work surface upside down with the muzzle to your left (assuming right handed).
You will see an orange firing pin sleeve (with firing pin inside) and a black plastic cap at the back of the slide. You need to remove the cap by sliding it up but it is locked in place by the orange sleeve, which is spring loaded to the rear by the striker spring.
3. So using a tool (like a punch or small screwdriver) slide and hold the orange sleeve toward the muzzle about 1/8 inch. Then you can slide the black plastic cap off the back end (you may need to pry with a small screwdriver to get it started.
Now look at the extractor parts in the picture in dberadslee's post:
http://www.taurusarmed.net/forums/smithing/51087-taurus-pt709-extractor-removel.html
With the black plastic cap removed, part 1.12 can move aft to relieve the spring tension on part 1.11 and the extractor (1.09).
4. To remove the extractor slip a very small screwdriver (like a jeweler's screwdriver) into the gap at the back of the extractor. This releases part 1.11 from the extractor and the extractor will slide right out. You might want to wipe out the extractor slot while the extractor is out.
CAUTION: the extractor holds the firing pin block in place. Don't let it fall out or lose it.
5. Slide the new extractor in. It will just click into place.
6. Compress the orange sleeve again and slide the black plastic cap back on. Once the cap is past the orange sleeve, you'll need to compress part 1.12 to get the cap fully on.
I wish I had photos because this is easier than it sounds. The only tricky part is holding the slide while you simultaneously compress the orange sleeve and slide up the end cap. Just don't lose the firing pin block or spring. Part 1.12 is captive and won't come out. The firing pin, sleeve, and spring won't shoot out but you can remove them while the black cap is off if you want to clean and lube them.
