Odds of Getting In
If you graduate from film school, become fluent in Avid and Final Cut Pro, get acquainted with graphics and sound software, and are prepared to work hard for little pay, you're ready to get in line.
Fortunately, editors have lots of opportunities to practice their craft. Craigslist is a good way to find quick pick-up work, low budget films, or industrials to supply income and also give you a chance to look over the shoulders of full-time editors. Look for apprenticeships, spend about five years as an assistant, and keep developing your chops at every opportunity. It's all about who you know; when a good editor gives you a chance to edit some footage on your own, jump on it.
Editing is a tough job and everyone wants to do it. The competition will be intense for a long time and the market growth isn't as good as that of most other career paths. It's not an easy field to get into, but a little perseverance will take you a long way.