How should I repair rotten load-bearing porch posts?
This could be a DIY project, but it's pretty big. Anytime you start messing with support columns you can get yourself into a big project. But, that said, this is most likely doable.

You need to get the bottom of the post off the ground with some sort of concrete footing and replace the bottom (or all) of the post.

Basically, if you hired a contractor, he'd prop up the roof using doubled 2x8's on each side of the post. Then he'd either replace the whole post or cut off the post about 2 feet from the ground.  He'd probably (based on code) also dig a hole and pour a concrete footing and then bolt the new post base back in. The size and depth of the footing can vary by local regs and the contractor's preference.

If it were me, I'd prop up the porch, take out a post, dig a hole (2 foot+, unless you are concerned about frost heave in which case 4 feet+), put in a sono tube up to about a foot above ground, fill it with concrete and put a new post in.

Based on local code, this would probably require a permit (but depends on where you are and the nerve of your contractor - personally, I'd do this myself without a permit...)

You reuse the metal bracket by embedding in the top of the new footing (sand it and paint it with rust proof paint), but you might not need it. Home Depot has lots of various bracket to attach vertical columns to footings. Also, google images is your friend on how this can look.