OK, so you have done all the round pen work, sacked your horse out so that he is bomb proof, taught him to lower his head and pick up his feet. It's time for that really big leap of faith to put a rider on his back for the first time.

This lesson presumes that you have worked through all the previous lesson well and feel confident that your horse is a willing partner. You should not try this if you are not confident in your ability to work with horses. Remember the old saying "Green on green equals black and blue!" If you are the green rider attempting to climb on a green horse, you are likely the one to become black and blue (or worse). At all times, you must be prepared for the unexpected. Pay attention to your horse. If at any point he starts to get upset, back up to earlier in the lesson, to a point at which he is comfortable, and pick up from there. The biggest mistake people make is to move through the steps too fast. The time you spend here is an investment. You can spend some time now doing it right or you can spend a lot of time later to fix problems (and maybe yourself). 

We begin with the horse in the middle of the round pen with a halter and lead. We calmly introduce the horse to the saddle blanket and take the time to make him feel comfortable with it as we rub it all over him. Then gently place it on his back. Next we introduce him to the saddle by carrying it to his front and just letting him look at it and smell it until he is comfortable.
Remember to take your time. We've put in some work to get this far and there is no need to rush now. Your patience will pay off in a smooth experience here today. When the horse is comfortable with the saddle, we gently place it on his back, being careful to not bang it around too much and possible frightening the horse. Now connect the cinch, but don't tighten it too tight. Praise and pet your horse often during this lesson, as he is taking big steps along with you. Now take the lead rope and walk your horse around the pen a few times. This gives him a chance to become a little accustomed to the new feeling of the saddle and cinch. Now tighten the cinch a little more and walk him around a while longer until he is comfortable. If you need to, tighten the cinch again, just enough to be sure it will stay in place and walk him once again.

It's time to take the lead rope off and move the horse around the pen on his own. Try to get him to move off slowly and walk around the pen a few times. If he moves off into a trot or canter, that is OK too, I just like to keep things moving slowly and incrementally if I can. Don't worry if he bucks a few times either, Just keep him moving. If he walks off, keep him moving around the pen a few times and then ask him to trot. Again, if he goes right to a canter, this is OK. Now keep him moving around the pen at a trot for a few laps and then move him into a canter. Keep him moving at the canter until he seem comfortable and not overly upset at the saddle.

Most horses will feel pretty comfortable at the walk & trot and generally don't buck. However, when we move the horse to a canter, most horses will buck a few times as they get used to the restrictive feeling of the cinch. I've come to believe that it is the pressure of the cinch that concerns horses much more than the weight of a saddle on their back.
Keep your horse moving at the canter until he is moving easily and without bucking. Ask him to stop and let him rest a few minutes while you pet him and praise him. He has just made a big leap in his training. Now repeat moving him around the pen at the walk, trot and canter. Horses rarely buck at all this second time moving around the pen. Stop him, pet him and praise him.
Let him rest for a few moments.

Now put the lead rope back on and hold the end. Go to the horse's near side and put the palm of one hand in the stirrup and slowly press downward applying some pressure to begin to accustom the horse to weight in the stirrup. Release and repeat a few times. Go to the off side of the horse and do the same thing. Repeat, alternating sides until the horse is completely comfortable with significant pressure in the stirrups on both sides.

Next, while standing on the horses left side, near his shoulder, turn the stirrup towards you and place your RIGHT FOOT gently in the stirrup. We use the right foot because it will keep our body closer to the front of the horse while we accustom him to bearing weight. This is a safe place to be incase the horse would kick with a back foot. It also seems a little easier for the horse to get used to bearing the weight when it is a little more forward. Hold the lead rope with lots of slack and the saddle horn with your left hand and grasp the cantle with your right hand. Gently step in the stirrup enough to lift your left foot about a foot off the ground and immediately step back down. Repeat this on both sides until the horse is comfortable with the action. Use your LEFT FOOT on the off side. Slowly increase the height that you are stepping until you can stand straight up in the stirrup with the horse remaining calm. Remember to work both sides.
Change feet. On the left side of the horse, place your left foot in the stirrup and stand straight up and hold still for a few moments (before you were stepping down immediately). Then step down and repeat on the other side. When the horse is comfortable with you standing in the stirrup for a while, gently lay your body weight over the seat of the saddle, hold for a moment and step down. Repeat from both sides and for longer periods of time until the horse is comfortable bearing the weight.

Remember to praise and pet your horse often to keep him calm and confident in you.
Finally, on the left side of the horse, step straight up so that you are standing in the stirrup with your left foot. Hold for a moment to be sure that the horse is remaining calm. Then gently and slowly, put your right leg over the horse's rump and sit gently in the saddle without putting your right foot in the stirrup. Be very careful not to bump the rump with your leg or foot as you step over. Sit quietly for 10 or 15 seconds and gently step back down. Repeat on the other side. Do more repetitions on both sides, increasing the length of time that you sit in the saddle with each repetition.

Give the horse a pat on the neck and yourself a pat on the back. You both have taken a very big step.

At all times, you must be prepared for the unexpected. Pay attention to your horse. If at any point he starts to get upset, back up to earlier in the lesson, to a point at which he is comfortable, and pick up from there. The biggest mistake people make is to move through the steps too fast. The time you spend here is an investment. You can spend some time now doing it right or you can spend a lot of time later to fix problems (and maybe yourself).