I’m not a doctor, and don’t have wrist/finger issues myself, so take my recommendations with a pinch of salt, but:
(1) Get enough sleep, exercise, eat healthy, try to avoid work/relationship/etc. stress if you can.
(2) Make sure you change body positions sometimes, and take breaks (don’t sit for 2 hours at a time!), walk around a bit.
(3) Make sure your display is at the height of your face, so that your neck and back stay straight, and you don’t have to bend over to see the screen. Laptops are really horrible for this (though that doesn’t stop me from working in coffeeshops on a laptop quite often; I just try to switch positions frequently).
(4) Make sure your chair is high enough / desk (or keyboard tray) is low enough that you can keep your arms in a comfortable position. Most office workers have their desks substantially too high and as a result need to bend their wrists awkwardly.
(4a) Alternately, consider an “ergonomic chair” like a saddle chair, kneeling chair, etc. There are a bunch of interesting possibilities at
http://www.ergodepot.com/category_s/168.htm – but I recommend trying to test these for a few hours or even a few days before pulling the trigger, as some designs might work for you while others might be terrible, and as a niche imported product they’re fairly expensive.
(4b) Consider working standing up, at least part of the time. Sit-stand desks make it really fast and easy to switch back and forth between sitting and standing positions without disruption of your work.
(5) Try to type with your wrists in as neutral a position as possible. For me, when using a standard QWERTY keyboard, I find that using my left index finger for c, middle finger for x, and ring finger for z makes it much easier to angle my hands so that my wrists are in a relatively neutral position (the “standard” typing style encourages a pretty sharp wrist angle in the left wrist). Alternately, a keyboard which is split, with the two halves either widely separated or rotated, makes it much easier to adopt a comfortable wrist position. Tenting two halves can also help a lot. To really go down the rabbit hole here, consider a column-staggered keyboard like the Kinesis Advantage or Ergodox.
(6) Try to find keyswitches which actuate reliably when pressed past their “tactile point” and then try to reduce the force you use and distance you press the key until you’re pressing the key as hard as necessary but not much harder – some rubber domes will not reliably actuate unless forcefully pressed all the way to the bottom, and this encourages typists to really smash them down hard (in my experience scissor switches and some high quality rubber domes can be decent). The impact at the bottom of the keystroke is where most of the shock comes from. Mechanical switches with a substantial tactile “bump” can be a big help here (have you ever tried a Model M, for instance? Or a clicky Alps switch?).
(7) Consider whether switching back and forth between mouse and keyboard is causing you trouble. In some cases switching from a mouse to a trackpoint, trackpad, “roller mouse”, or trackball can be a big ergonomic advantage. Even just trying to learn more keyboard shortcuts might help considerably. Some people have had good luck with reducing the size of their keyboard so the mouse isn’t as far away, or even learning to use the mouse with their left hand.