Hey Dude,
I had tendonitis in my wrist a while back - mine was from hammering & shovelling too much while working on a building site. I was affected on the thumb side of my wrist with a constant ache, plus the joint was very stiff and painful to move, especially in the mornings (when it felt like the whole joint has seized up and fused together). If this sounds like what you've got then there's a few things i found helped to sort it out.
Go to a physio. I tried to avoid doing this for ages because of the cost, but I only needed two sessions (about 3 weeks apart and religiously doing the prescribed excercises in between) to get it sorted. I was given ultrasound and got manipulated and massaged a bit. In between times I stretched my wrist by supporting my arm out in front of me (thumb side up) and tucking my thumb into the middle of my fist then bending my wrist to push the little finger side of my hand towards the floor until I could feel a stretch on the thumb side of my wrist. While stretching it also helps to massage the tendons - rub your other thumb perpendicularly across them (ie rub left to right with arm pointing forwards). Do this gently for up to a few minutes at a time, three or four times a day. I've also heard that icing the joint helps the symptoms, but I don't know if this actually helps recovery or just provides pain relief.
I found that doing all that lot got me back climbing pain free again within about six weeks of first going to the physio and I've had no repeat problems, however I was constantly nervous about over stressing the joint when I started climbing again - I guess thats the same with all injuies though.
Hope that lot helps, once you're on the road to recovery the worst part is the constant stream of wanking jokes coming from your mates (how else would you get an overuse injury in your wrist?). Good luck.