writing-with-science Answer:

Hey I am really sorry, idk when you sent this but tungle.hell never notified me so I only found out about this ask relatively recently.

Anyways, in prosthetic limbs in general, there is usually a bit called a pylon. That is the internal frame for structure and support. Nowadays they are made with carbon fiber though they used to be made with metal. These are then covered with a protective sheathe thing that can either be kind of rubbery or hard plastic depending on the style wanted

The socket is the bit that goes on the residual limb and the suspension system would be the straps and stuff that keeps it in place. 

Now as far as how prosthetic arms are used, there are body controlled mechanisms external controlled mechanisms, and myoelectric mechanisms, (these are relatively new and quite spendy) 

Body controlled prosthetics involve wires that are attached to other parts of the body (such as the opposite shoulder) and moving that body part controls the limb. This would take some practice and often a hand shape would have to be simplified into a hook. That would look something like this:

A externally controlled prosthetic would kind of be like having a remote control for the limb. It is heavier than the body mechanism and more expensive. The limb would be controlled with a different body part by flicking switches and pressing buttons (so to speak, that body part could be a shoulder or something) or if the residual limb has some muscle control, that could also control it. 

Then the most advanced, and most expensive, would be myoelectric. This is the kind of futuristic robot arm that hopefully will be more available to more people in the future. This is where there are electrodes that attach to the residual arm muscles and when these muscles are contracted, the arm moves. This is also battery powered. This gives a lot more control and essentially you could kind of move the limb like you used to without even really thinking about it. Of course this technology is relatively new so you wouldnt have as Much control and precision as a real arm, its certainly a lot better in control and normal movement than some of the others.

so really it depends on what type of prosthesis you want to give your character. And a lot of these vary depending on who is making them so its hard to give super specific parts and details but those diagrams should help.