Two basic approaches:
Slab it on there with the cutting edge at the desired angle. Works fine for small edge breaks, particularly on the OD, typically the end of the part. With proper grinding, a thread relief can be cut in a single operation if the left edge is square to the axis of the work, and the right side at the desired angle (typ 45° for UN threads). Often, if the relief is wide enough, straight groove tool can cut the relief and a tool similar to a threading too, except 90° included, can be used to slab the leading and trailing edges. Thread reliefs aren't always that wide in practice though.
Profile, or compound it on: Here you have more flexibility. You can catch an OD edge with a boring bar by simply reversing the spindle and using the compound to move the tool. I do this quite often. I'll finish an OD, and proceed with the bore, and when I compound the chamfer on the ID, I'll just reverse the spindle and to the OD. The only slightly tricky part of this is determining exactly when you have removed all of any burr that may be raised up, so that you can start making measured moves to hit a specific size. If you have good eyes and a soft touch, it's not hard to get used to. Also, you can easily swivel the compound to whatever angle you need and not have to grind a special tool. Another advantage to this method as opposed to slabbing is that you can compound a larger bevel or chamfer without chatter.
Sometimes, if it's my own work, I'll cheat on the back side of a thread. I will use a 35° diamond inserted tool to finish turn, but have the compound set at 45°. When I get to the shoulder I am threading too, I simply plunge the turning tool in, and pull it away from the shoulder until I get the width of relief I want. The holders are not neutral, so they don't really like cutting wrong-handed, but they will well enough to do a thread relief. That angle is NOT 45°, but after it is threaded, so little of that surface remains, it is not a problem.
There's more to tell, but I'll let others chime in too.