It depends somewhat on your goals. Are you interested in picture editing? Sound editing/mixing? Color correction?
I’ll assume picture editing–the “putting together the story” kind of editing.
Do you want to be a movie editor? That’s difficult to break into. In that case film school is not a bad idea; you can learn a lot of things on your own, but making student films will teach you the collaborative process; you will get access to internships which will help you; and your classmates will form a cohort that helps each other as you all rise in the business. Also, top film schools will have really top teachers who will mentor you/help you make connections; and talent agencies scout these schools for promising young people. That’s less true for editors than it is for directors though.
Are you interested in TV? I know mainly about reality TV. I run into a lot of smart, well-educated, motivated, talented people from schools with communications programs like Emerson, Ithaca College, and San Francisco State. The same applies here to internships, working with others, and making connections for life.
There are many, many, many jobs in LA for reality editors and the pay is good (though the hours can be awful). Some editors I know have transitioned into half-hours and a very few into hours. There are many fewer jobs like this and the talents required are different; the kind of thing you learn more from making short films–working with multiple takes, choosing best performances, etc. (Though many “reality” shows are so fake you’ll do the same thing.)
You will need to know a great deal of technical stuff about how edit systems work. By far the most common is Avid. FCP is a toy. I know many people like Premiere; I have no experience with it but I don’t know of any production companies that use it. Maybe it’s the future, but the present is Avid.
Your first job will likely be a post-production assistant, maybe on a show, maybe at an edit facility serving many shows. You’ll do things like ingesting and transcoding footage and dealing with technical issues. Also getting lunches and scutwork. It might be a night job. Then you’d progress to Assistant Editor where your job would still be largely technical, with some story responsibilities. On reality shows AEs often cut “extra content” for the web and international versions.
Then you’ll become an editor when someone takes an interest and you demonstrate some ability. Many reality production companies look out for talented assistants and promote them quickly, though you’ll make less than an experienced editor. It will still be a really good paycheck.
Hope this helps.
ETA, you’ll also need to know hardware stuff, like configuring a RAID and how to set up a system and troubleshoot a mixing board and so on. When you become an editor you will forget every single technical thing you ever learned and rely on an AE 