In order to get into a magnet school, you must apply using the eChoices application that comes out in the late fall each year. The application process is simple - all you have to do is fill out the form and send it in. The application brochure will be mailed to your home if your child already attends an LAUSD school. You can also pick up forms at your local LAUSD school, LAUSD offices, and Los Angeles Public Libraries. If you're picking up a form, try to do so shortly after the brochure is published as facilities do run out of them.
You can only apply to one magnet school each year, which makes things a little tricky because your chances of getting in depend in part on how many other applicants there are. The eChoices brochure that contains the application indicates how many slots were available at each school the previous year, and how many students applied for them, which helps you to see the odds of getting in.
However, if you've heard parents groan about the magnet school application process, it's because of those odds. The odds depend partly on a lottery, and partly on a priority points system. And that points system is complicated enough to warrant its own post. You can learn about the points system here.