you’re saying you have a problem but it’s hard to help when so little information is provided. so, what exactly is not working? at which step you think unexpected results occur?
assuming that you have little experience here some hints:
make sure you’re in the right “mode” when parenting. that is, leave edit mode for bones or the mesh (TAB; if your bones are pink then you’re in edit mode). select the arm object, then shift-select the armature (which should contain ALL bones - fingers, thumb etc.) and then press ctrl+p. choose “armature” and then “don’t create groups” (as you have already created them). parenting is done now.
to test press first “A” (this either selects all objects, or if one or more are slected it deselects them), then select the armature. press ctrl+tab to enter pose-mode. select any bone and rotate it. if you did everything right, the mesh should deform accordingly.
hope that helps