When you first start to ride, make sure you are wearing the correct equipment and make sure the horse is the right size for you. When you learn to mount a horse, make sure you put your left foot in the stirrup first and then 3..2..1, and on you get. Make sure you hold the reins tight and correctly. When you are learning to walk, try and keep an up right position and gentle kicks and maybe even have an instructor leading you.
Once you are confident with the walk, move on to the trot. The most important thing about the trot is getting used to the horse's beat. Try a sitting trot first to get use to the feeling and then move on to the rising trot and remember the 1..2 beat.
When you move on to canter, when you get into the corner of the riding school, sit up straight, sit on your bottom and kick. When you are in canter, try and sit squeezing your legs to stay on the saddle. Remember to relax in canter and give the horse it's head to prevent bolting.
When you are confident with all of this, you are ready to move on to a jump. Try jumping over a small cross or even a pole that's practically on the floor. Try to trot into it first, maybe have a leader if you don't feel confident. When you're coming into the jump, you need to relax, keep kicking the horse and keep a tight rein. When your going over the jump, lean forwards slightly and give your reins allowing the horse to have its head, so better jumping. After the jump, sit back up to your normal position and then do the same again in canter.
Remember this takes a lot of time and practice, so you're not going to pick it all up in a day. This is more for English riding then western, but I hope this helps.
Check out these photos.
This is my granddaughter. I'm teaching her how to ride horses. This is her 10th lesson and she is doing great. We also have a paint pony she is teaching it how to neck rein and ride so the neighbor kids can ride with her.