Learn how to use one or more video editing programs. There are several available editing suites, ranging from low-end -- such as iMovie and Windows Movie Maker -- to high-end, such as Final Cut Pro.
Create trailers for movies that have already been released, using your editing software. This will allow you to create an editing reel you can show to possible employers. The best movies to make trailers for are those that did not have a particularly memorable marketing campaign.
Send your reels, in DVD form, to trailer houses and marketing departments for movie studios. Both entities hire trailer editors. Even if the possible employer is not hiring at the time, they may still keep your reel on file for future consideration. Even if you are not hired as a salary worker, you may get a job doing freelance work.
Create a new, professional reel once you have done enough work in the industry. This will allow you to get a higher paying job as a trailer editor, or strike out on your own and found a trailer house.