Acquaint yourself with the process of making movies. It is hard work mixed with lots of down time. One good way to gain experience is to act in student movies. There is usually no pay and the filmmakers themselves are learning the process as well, but it is a great way to experience all aspects of film-making. You'll most likely do auditions for the student filmmakers. If you get the part, you'll be surprised to find that many student film sets are well run, and the experience is a lot alike the one you'll have on a professional film set. Also, make sure you have high quality copies of the films you appeared in. Most film schools require their students to give you a copy of your work. Get a friend or a film student editor to help you make a talent reel. It will look better and you will come off as more professional if a non-actor helps you focus your reel. This reel should include snippets of scenes you've appeared in, preferably with a little bit of context. Let some scenes play out to show off your talent, and intercut it with some nice-looking shots of movement to make it dynamic.
Get an agent or manager. The easiest way is keep going to auditions, be friendly with casting people and hope that you land small projects, minor parts, commercials or that your student film gets a lot of exposure. You'll never know what project will get you noticed. Agents and managers don't often respond to solicitation. In fact, they tend to frown on it. With good exposure, agents and managers will seek you out.
Be professional. While making movies is fun, remember that being a young movie star is the same thing as being a young professional. Take the job seriously. Don't horse around too much. It is OK to be friendly with everyone there, but remember that they are on the set to do a job and may not have time for you. Some directors even ask their crew to keep a distance from the actors in order to create a more personal and intimate working bond.
Follow set politics. Parents, you are on the set as guests. The director, producers and first assistant directors are in charge. If they ask you to leave, do not take offense. It is often hard to focus for a young actor if her parent is around, and it challenges the authority of the director. Film crews talk about "set moms" and "set dads." This is not a good thing and will only dissuade others from hiring your child. If you as a parent is invited to watch your child perform, do not interfere or give your opinion without being asked.
Seek out auditions, gain experience and keep working. Being discovered is more luck than anything else, but the more work you put in, the better your chances are of being noticed. And once you have been noticed, keeping working. If filmmakers have a good time working with you, chances are they'll recommend you to their colleagues. Remember to have relationships and friends outside the industry. It will keep you grounded and give you more experience to work from when you are on set.