Mounting your horse can be very important. This, and when you are first on your horse, is when the horse first gets to know you. Even if you're not sure of yourself, you still want to act like it! Horses are not as stupid as some people think - they will sometimes take advantage of unexperienced riders.
So, you always mount on the left side. Take hold of your saddle horn and the cantle, place your left foot in the stirrup, and just pull yourself up! Swing your right leg over the saddle, and gently seat yourself in the saddle. Place your right foot in the right stirrup, and your ready to go! Just remember: some horses will automatically start going once you're mounted. Make sure you don't let them get away with it!