ALWAYS REMEMBER TO WEAR YOUR RIDING HELMET WHEN ON A HORSE! IT CAN SAVE YOUR LIFE!!!!
This picture is a good example of what you want to achieve as far as riding positions go. When you're sitting in the saddle correctly, there should be an imaginary line from your hip to your heel, and from your toe to your knee. Your back should also be fairly straight and your head should be up - looking in the direction of travel. Throughout all riding positions, your heels should be down - this is your base of support!! 'Jim' has a good overall position in the saddle that will help him ride correctly.
What in the world is 'Jim' doing???!!! Heres a bad example of how to sit in the saddle!! DO NOT DO THIS!! This is usually referred to as the 'Armchair Position'. It looks like you're sitting in an armchair! and can be very dangerous, should something unexpected happen. Notice how 'Jim' is leaning forward, there is NO 'line' from his hip to his heel, nor is there a 'line' from his toe to his knee! If his horse bucked, 'Jim' would find himself eating dirt!! Compare this set of diagrams, with the first 2 at the top of this page!
When riding, keep your head up and your eyes looking forward - in the direction of travel. If you start looking towards the ground, your whole body will start to lean foward, you won't be able to see properly to steer the horse safely, and you'll almost certainly find yourself back in the armchair position! PUT YOUR HEAD AND EYES UP JIM!!!!
During your first few riding lessons, apart from other pointers, you'll most likely hear your instructor tell you to stop gripping the saddle with your knees. If you grip with your knees, you'll ultimately push yourself up out of the saddle and the ride will very very bouncy and uncomfortable for both horse and rider! Its almost like a chain reaction: 1) You grip with your knees, moving your leg up and losing the contact your leg had with the horse. 2) Because your knee is gripping the saddle, your heel will ALWAYS come up and REMEMBER!! Heels down = Security in the saddle!!! If your heels come up, it greatly affects your position. Lastly, 3) Because your seat is so insecure after 1 and 2 have happened, you will push yourself out of the saddle. This makes the sitting trot impossible to ride because you'll be bounced all over the place, and your horse will not be happy because he can feel your every move through his back! You're also at risk of losing your iron (refer to glossary for terms). What 'Jim' is doing is very unsafe!
If you plan to learn how to jump, you'll need to know the proper jumping position. Its quite a bit different from the first pictures (basic riding position) but it serves very well for hopping over fences and other obstacles. In the basic jumping position, your body should be in the shape of a sideways 'W' - as you can see from the second picture! Notice how there is still a line from your heel to your hip, and from your toe to your knee! The rider (or 'Jim' in this case, lol) raises his behind out of the saddle just a little bit so that his knees and ankles will act as shock-absorbers when the horse takes off and lands. You look between your horses ears, still in the direction of travel and your body leans forward just a little bit, so that you stay with the horses motion. This stops you from being left behind should the horse take off too soon or too strongly.
Hope this helped you!!
Please remember that I am NOT taking the place of a qualified riding instructor. I'm only offering my advice and help. (please read the disclaimer on my tips index).