Basically, drill a hole going to the bridge, run a wire through it, and solder it to the bridge.
If you've got something like a Les Paul with a TOM bridge, it gets hairy. You've gotta pull the bridge post stud out of the body and drill to that. I don't feel comfortable doing it, and one of the two reputable techs in my town didn't, either. On top of being difficult to do, it's possible that you can take up finish or chunks of wood pulling the stud out.
Something like a Hipshot is easier, and a trem is even easier than that. With the trem, you just have to get from the control cavity to the trem cavity. Like in this picture, only the cavities are usually even closer on more modern guitars: