The old school prosthetics tended to be strapped on in a way that let you use other muscles to operate the grasping part. The typical ones you’d run across were hooks. They had two sides, and you’d essentially flex your upper arm to spread or close them (over simplifying, but that’s the gist).

And that’s in terms of stuff that did move. Some were purely aesthetic, others (like the classic pirate hooks) served to allow a range of tasks, but didn’t move. There’s some examples of really old prostheses that were remarkably dexterous, but they tended to be one-off items.

In terms of the full on mechanical hands, those are relatively new. They’ve been developed for decades, with a handful of methods used to try and bridge the gap needed what the person wants to do and the movements the device makes. Anything from picking up brain signals to electrodes that detect muscle twitches at the site.