Believe it or not, getting off a horse incorrectly can get you hurt (We won't count the time I tried to vault off at a canter and ended up in the ER, because that was a kid showing off ;)).
In a western saddle, you remove your foot from the right stirrup and slide partly out of the left stirrup, hold on to the horn with the right hand, and then swing your right foot over and step down out of the stirrup.
In an English saddle, you remove both feet from the stirrups, lean forward with your left hand on the saddle, swing your right leg over and slide down.
You never use the step down dismount from an English saddle - it's almost guaranteed to break the saddle sooner or later by twisting the fragile tree. Dismounting at speed is a little different - I'll talk about that (and how I ended up in the ER) soon.