Good advice here already. It depends on the individual horse, and on how he has been handled. You have to have a “good” relationship with the stallion, and by “good”, I mean “fair”. He has to be treated “fairly”. You can not be “rough” or “harsh”, or “mean” or “unfair”, but you have to be consistant. So, much like other horses, but more so, because if he is not “with” you on this job, he can be “against” you, which is not pleasant or safe for you or for the mare being bred, more so than other horses. The two of you have to be a “team”, working together, on the same side, to get a job done, safely, and accurately. A breeding stallion can be quite “intense”, and extremely “focused” on the job. In this respect, he is a bit different to handle than other horses.
I’ve stood two TB stallions at stud, one for sport horses, one for race horses (which turned into sport horses later in life LOL). So I have no personal experience with AI, but plenty with live cover. Both stallions were easy enough to handle hand breeding through the years. Both ended up pasture breeding also, and a person would have to check for nuts to even know they were stallions most of the time. One thing is for sure, there is no way to teach a stallion manners like turning him out with some mares, because they will teach him manners better than any human ever can. These guys never needed teaching, they were both always a well mannered guys. The first one had a career at the horse shows while also breeding mares at the same time… nobody much even knew he was a stallion at the shows, he didn’t make it obvious. If a sport horse stallion can’t do this, he isn’t stallion material, IMO, because disposition and personality is just as important as all other things that a mare owner is looking for.
One thing that I did notice with both these guys was that they had preferences. The one who went horseshowing, he would pick out his favourate mare at the show, and watch her, quietly, but intensely. He would always pick a mare with flashy colours, pintos, appy, or something with lots of socks and a big blaze etc. But he would “worship from a distance”, and watch her if she was jumping a course, or walked by. Just watch her. He didn’t pay any attention to any other mare at the show, just his “choice” mare. The owner/rider of the chosen mare had NO idea this was going on, there was no vocalization or physical signs, just his attention, his ears and his eyeballs. I’d just have to be aware of it, and bend the stallion’s head away from her if she came close to us, to remind him to pay attention to me, and that he did not get to go and “chat her up”. The other stallion, he did NOT like chestnut mares. He’d do one, if that was all there was. But if he saw another mare, he’d forget about the chestnut one that was in heat and ready to breed, and want to go look at a dark bay mare instead. So, no distractions for him, to keep him on the job.
The worst stallions mannered I have encountered have been those involved with AI collection… I presume because they do not have to have a relationship with the mares. One stallion was shipped from home to go to the collection place, and bashed himself to injury in the trailer on the way, went “crazy” in there. Another one savaged mares (and humans) when live cover was attempted, and attacked the dummy with urgency to the point where a human needed to not get in his way until he was finished. (Why do people want to breed their mares to horses like this??). Anyway, as you can tell, I do not like AI, for the stallions, or for the breed, for multiple reasons. But of course, I am outnumbered in this opinion. As the genetic flaws and personality flaws pile up due to AI causing a reduction of genetic diversity as they already are in breeds that allow it, and a proliferation of poor dispositions from stallions who can not safely live cover, it will become even more obvious, as it has already in dogs and cats, IMO.
PS. If you want to learn about handling stallions, go and visit some stallion managers in your area who you feel are skilled and experienced, and ask them about it first hand. You will get good tips.