I am in the process of learning blender and I am trying the tutorial that allows you to animate an arm. I am having trouble parenting the fingers to the hand. I go into the armature bone list and when I select the “Fing3A.R” bone and hit “child of” it does not give me a choice of the hand bone.

Are all the bones in the same armature? If you go into object mode and select the finger, is the hand selected too? If not then you will need to join the armatures (Ctrl+j in object mode). This will delete your constraints though.

The best way (that I have found anyway), is you place bones where you want, and when you want to add more (eg. add fingers after you have placed and setup the arm and hand bones) is to select that armature, go into edit mode, then spacebar>add>bones. The bones you then place will be part of the current armature.

That helped alot! Now I am having difficulty with the mesh moving with the armatures. The armatures move wonderfully (except I can not make the wrist bend and twist). I have assigned each bone to the mesh that it is going to deform. I can hit the select button and see that they are assigned properly. The only thing that I can think of, is that in the tutorial at the end, it says to exit the edit mode and parent the arm to the armature. I am unsure what to do here.

You need to select the armature, then select the mesh and press ctrl+p to make the armature the parent of the mesh. When you do that a menu pops up, choose “armature”, then another menu pops up.
What happens is you will create groups of vertices from your mesh, and assign them to various bones. This last menu gives the option “don’t create vertex groups”, “name groups” and “from nearest bone”. Or something like that anyway. I have been using “name groups” to create the names of the vertex groups for me, but not assign any vertices to bones (automatic skinning gives wierd results).

This tutorial (skinning part is near the bottom) should have all you need.