How long it takes usually depends on your climate and breed of horse, but for us, the horses are fuzzy in April and glossy and sleek in may or june. To speed it up, groom every day, or as often as you can, to get all the loose hair out.
Around here, shedding is usually done in late April/early May. But it really depends on how many daylight hours your horse is getting. So, if he/she is under lights, he/she will shed a lot faster than a pasture kept horse. I've found that using a shedding blade daily really helps and once she's about half-way shed out, I usually give her the first bath of the season which takes care of a lot of hair.
Shedding starts when the days start getting longer. So my mare was shedding in December. I use a shedding blade on her, and vacuum her to get all that loose hair out. It's starting to seem like the hair is not coming out as much now, but it is annoying, I have hair every where.