You can do wrist 'curls' front and back. Basically put your wrist on your knee with your palm facing up and holding a dumbell in your hand. Lower the dumbell using your wrist until your wrist is bent as far as it will go and then curl the wrist back up. For your fingers you can open them and allow the dumbell to slide out to the last knuckle then close the fingers and curl the wrist up. That is the forward wrist curl. For the back wrist curl place your wrist on your knee with the palm of your hand down and the dumbell in your fingers; curl the wrist up until you can't then lower the weight as far as it will go. This develops the forearem, tendons, and wrist. You may not see any development in the actual wrist area as there aren't many muscles there but you will strengthen the tendons and joint.
For more exercises Google wrist exercises on the Internet.
Start hanging from a pullup bar, not more than a minute or two per day. Every other day is fine too. When that's too easy, start hanging from a towel that's hanging over the pullup bar.
Start learning how to do fingertip pushups- against a wall to start, then fingertip pushups against a table, then on your knees, etc. Just a few at a time (3-5).
These two exercises will increase your grip and your straight-finger strength. They will increase the size of your forearms and the strength of your tendons. They will not make your wrist bigger. Your wrist is pretty much all bone and sinews, and making that bigger is nearly impossible (I don't want to say completely, but pretty near).