Try doing push ups on your knuckles. Form a fist and place the face of the fist (the area of finger between the middle and lower knuckle) on the ground while you do your push ups.
There are other designs you can get at your local sports store.
Also grippers work really well. Walking push ups on your fingers work the wrist really good. Holding a 3-5 lb weight in the palm of your hand for as long as you can will help.
There are a few easy things you can do to increase your wrist strength. The classic "roller" where you use a piece of rope attached to a broomstick or dowel, which is tied to a weight is probably the easiest and most common. I wouldn't suggest buying a premade version, because I think you can make your own, customized to your hand size, at least as cheaply. Wringing a towel is a similar exercise, as well.
You can also use a staff or pole; hold it near one end, and try to keep it straight and level. Once you can simply hold it, you can start moving exercises with it.