I think riding Side Saddle is so graceful and elegant! The side saddle has gone through a lot of changes over the years - changing from a basket type seat that sat the rider sideways to a flat seat with horns positioned to sit the rider straight to the front of the horse.
A friend at the yard five minutes from ours rides side saddle. Her horse is beautiful and they look so good together! The lady in question has ridden side saddle for numerous years now and has done cross country and hunting, while recently trying her hand at side saddle dressage.
You can school your horse the same as riding astride. Same process just using the different commands. I was lucky enough to be offered a shot of riding side saddle and boy was it a weird feeling! To mount it is with a leg-up or mounting block. You then sit on the saddle as if you are riding astride, and then swing your right leg across the fixed head thingy.
Shoulder position was the part I found difficult at first. Your right shoulder needs to go back, so that both shoulders are straight and forward facing. I felt I was concentrating really hard to keep my shoulders straight
I used a whip where my other leg should have been for aiding for bend etc, my friend stressed this is why a horse should never be fearful of a whip.
Walking round was fun just takes ages to get used to the position but once you have it, it feels really nice

My constant reminder was to stop trying to feel with my leg that was swung over

Trot was really weird! And I didn't feel confident to try anything else.
And the really weird bit of it all was dismounting - where you take your foot out of the stirrup. Swing your right leg over the pommels so both legs are on the nearside, and then slide to the ground. BUT at the same time you need to turn as you slide to face the front.

It took me ten minutes to get the instructions straight in my head before trying to dismount
All in all a great experience and if I had the time and money I would definitely go for side saddle lessons at the local school! But until then it was just a great experience