How long's a piece of string, Helen!
It's entirely up to the stud and/or mare owner - some studs, such as Cheveley Park, don't offer boarding for visiting mares, so the mares have to be boarded elsewhere and 'walked in', ie, they'll be boxed over at a pre-arranged time with the Stud Groom, once he's been informed the mare's in season and her vet has performed an internal exam to see if the follicle is at the right stage for optimum chance of a conception. Also, some breeders save costs by walking their mares in from home - I've a neighbour who walks in her mares to Tweenhills, which is two hours away. I'm not keen, as I think while you save on keep bills, you can lose pregancies this way too on long journeys - a mare's temparature only has to increase by more than 1.5 degrees to affect an embryo's viability dramatically.
Alternatively, studs like the National Stud and the like offer boarding facilities 'on site' and the mares are teased on a regular basis. As they come in season, they'll have their internals and, when the vet he say "Yes", then the stallion will cover the mare.
Mares are scanned to see if they're in foal at around 15 days - if they are, they're re-scanned at 26 days if they haven't 'returned' (ie, come back into season) to check the size of the foetus and its heartbeat. The mare will be re-scanned again at around 36 days and it's safe to ship her home any time after 42 days. Of course, mares do return and do have to be covered on successful heat cycles.
If you're breeding for the Flat, you tend to draw stumps by the middle/end of May, as late foals are not commercial at the sales. It's entirely different for NH horses of course.