Practice, practice, and more practising is the key. I started when I was a kid by roping an old saw-horse. Before you hop on that horse and start swinging a rope, it's a heck of a good idea to get him used to it by spending time swinging it (not walloping him with it) in his general vicinity.
The basic idea is to desensitize him to that thirty foot "snake" you've got in your hand.
Usually, I'll just tie up the colt to the fence, set up that ol' sawhorse and start making catches on it. Some horses take quite a while to realise that you aren't going to hit them with it (and that it isn't going to "bite" them).
Be prepared to be patient, as this may take several hours over a period of days for some to become accustomed to it.
Next thing I do is to climb aboard, and get him used to the sound and sight of me swinging the loop while I'm sitting on him. This can usually be a little nerve-wracking to most horses, so just be patient, and work extra hard not to nail him with it (or you'll have confirmed his fears). Again, this may take awhile for him to become used to it. Be prepared to sit tight. Next you have to teach the horse to accept your throwing the loop off of him.
A good rope horse also need to learn to "rate" the stock, which basically means that he knows the distance he needs to be from it, when to speed up, when to slow down, and when to stop. He'll also need to know what to do when you catch the calf, and you'll need to learn how to keep that rope from coming around you and clotheslining you out of the saddle (never a fun way to fly) and then there's always the chance that the calf will duck around him and run that rope up under his tail (usually a recipe for a NFR saddlebronc riding exhibition), and heaven forbid that calf runs under your horse's belly.
Ellie, roping can be a lot of fun, but there are also a lot of ways a person can be hurt, so my advice to you would ulitimately be that I HIGHLY recommend that before you jump aboard and start off swinging in pursuit of a calf that you take the time to meet some of the people in your area that have experience with roping horses.
Their experience can save alot of wrecks for you, your horse, and the stock (remember, always always always keep your thumb out of the dally). Most people that rope are happy to pass on the tradition to people that are willing to learn. Find a good old hand in the neighbourhood, and usually they are quite content to teach, as long as you are consistent in your desire to learn and take constructive criticism.
Just remember, kiddo, that like all good things, it will probably take a bit of time to become proficient at it. Don't get discouraged, just keep on practising. It's great fun, and I sure hope you give it a whirl.
Best of luck to you.