there's a few schools of thought here.
1 you can use a leader straightener, or your fingers to create friction, heating the leader and thus straightening out the coils. I do not subscribe to this idea, as I feel it's unnecessary stress.
2 stretching the leader. all mono stretches, and this will straighten it as well. it causes stress, and as you stretch it out, either multiple trips out or fish, it will weaken. I do this using tapered leaders the first time. a good stretch from one end to the other, after that I will lightly stretch if it's sat on a reel, but not as hard as the first time. I do not replace leaders after every trip, that is too expensive for me. I usually get at least 3-6 fishing days out of a single leader.
3 if you're not fishing dries, you can use furrled leaders for the ultimate straight and supple solution. I've heard a lot if good things, but haven't gotten to try one yet. they will sink if not treated with flotant, so aren't good for dries. also even when treated, need to be retreated multiple times through the day.