I fairly often ride horses who's back is not far below the top of my head...my trainer's horse, when tacked up, has a saddle seat level with the top of my helmet (which is about an inch thick!).
Even a small horse can be a long way up, leading to the (mythical) idea of knights in armor having to be winched into the saddle.
So, how do you get up there?
The correct way of mounting in English tack is to stand on the horse's left (we do everything from a horse's left because of where a sword hangs when you're wearing one) facing towards its rear. You then put your left foot in the stirrup and your left hand on their withers (not the saddle), and hop forcefully around to bounce into the saddle.
Western riders stand facing the horse or slightly towards the tail, put their left foot in the stirrup, their left hand on the withers and the right on the saddle horn, hop a couple of times and half hop, half pull into the saddle.
However, many people use some kind of mounting assist. A mounting block is the most common when departing from home - this is a wooden or, these days, heavy plastic stepped platform that allows you to just step into the stirrup (Unless you're riding a huge horse, in which case you might still have to pull yourself up). On the trail, a good horseman will always look for a mounting assist...standing on a rock or log, or putting the horse in a ditch or downhill. Mounting straight from the ground can make your horse's back sore and, especially in English, shorten the working life of your saddle.
I'll talk about assisted mounting in the form of a leg up, how knights really got into the saddle and the correct way to get off next week.