There are, in general, four approaches that are commonly taken.
The first, mostly used with solid axle designs, is a floating rear caliper mount with horizontal dropouts. In this type of design, the rear caliper mount fits into a slot aligned directly with the rear dropout. Part of it nests around the axle so that the caliper maintains a fixed distance from the axle, ensuring correct alignment with the rotor front-to-back. There is usually a bolt and nut that go through both a hole in the chainstay and a slot in the rear caliper mount which is used to fix it in place once you have the wheel installed and the belt tensioned properly. This design makes it a bit tedious to remove the rear wheel, and it requires a frame that’s designed for it, but it’s one of the most inexpensive options from what I’ve seen.
The second is a variant of the floating mount concept commonly called slotted dropouts. These are used with QR and thru-axle designs, and essentially just let you adjust the linear distance between the rear axle and the bottom bracket, allowing for adjustment of chain/belt tension. Most of the good ones have caliper mounts for a rear disk brake caliper on the sliding part so that it will stay the correct distance from the axle as you adjust tension. Just like with a floating caliper mount, these also require a frame designed for them.
The third approach is an eccentric bottom bracket, which is mostly used with QR and thru-axle systems. Again, this is mostly just providing a way to adjust chain/belt tension, but unlike slotted dropouts or a floating caliper mount, it doesn’t change the position of the rear axle, so you can just mount your rear caliper directly on the frame. I’ve not dealt with an EBB in such a setup myself, but from what I’ve heard from friends who have, they’re also a bit of a pain to handle when removing the rear wheel, because you have to loosen the BB to remove the wheel, then adjust it correctly again when reinstalling the wheel.
The fourth option is to just use a chain tensioner. This obviously only works with a chain drive, but it’s likely the most practical option if adapting a frame designed for a RD setup to an IGH. Just like an EBB setup, the rear axle never moves, so the caliper is just mounted directly to the frame.