From what I can tell, people get into translation by one of two avenues: they attend translation training courses at universities, or they “fall” into it after becoming thoroughly proficient in two or more languages and working in other fields, doing translations on an ad-hoc or informal basis for their employers, friends, or colleagues, and find themselves increasingly in demand afterwards.
I can’t speak for the translation training avenue, but I can speak for the latter. Both my grandfather and mother were noted translators and editors in their time. Both spoke multiple languages (in my mother’s case, with a perfect native accent in each one—an uncanny gift), both their homes (and conversations) were full of books and other writings in Hebrew, English, German, Russian, French, Spanish, so my sister and I absorbed language and writing ‘by osmosis’, as it were.
For years, I kidded myself that I could pursue a more ‘practical’ professions, but by my mid-thirties I inevitably found myself drawn, first to technical writing in the Israeli high-tech industry (where bilingualism was a basic requirement), then about a new method for mastering the Hebrew script, then to translations outright. At first it was helping my mother with her ‘overflow’ work, then those clients began to come back to me specifically, then their friends and colleagues, etc. In short order, it became a full-time occupation—and I’ve never looked back.
The route for ‘falling into’ translation will vary from one person to the next, but what you’ll probably find in common in all cases is an abiding interest in language in general; a fascination with how people of all walks of life express themselves (coupled with a compulsion for correct usage in academic writing); an attempt to pursue another vocation before giving in to one’s true calling; and of course, a thorough, native-speaker command of the source and target languages.
If these features don’t describe you, you’re probably better off going the translation training route—or pursuing some other vocation, that you’re truly passionate about (the test is simple: would you do that work even they didn’t pay you?).
As to how you would set yourself up in the business of translation, see.
(Originally written in reply to a question at Quora.com).