Vertex Groups are found in the Edit buttons. What you do is go into edit mode, selsct the appropriate group of vertices, create a new group and click on assign to put the selected vertices into that group. The way groups work is that if a group has the same name as a bone than that group will follow that bone.
Vertices can form part of more than one group (and their weight is distributed accordingly) You could also use groups to save selections by give a group a name that does not belong to any bone (usful for RVK’s). It is important to remember that the group will only be affected by a bone that is part of the armature that the mesh (with the group) is parented to. In other words if you have a bone with the same name but in a different armature than it won’t be affect the group.
There were some good tuts about vertex groups/weight/painting but I didn’t keep the url’s. I’m sure if you check on the pages where some of the other users are posting links to tutorials you shouldn’t have any problem finding them!