I am a medical transcriptionist. I've been doing it a couple of years, working from home, and I like it a lot. It's one of the few work-at-home jobs that ISN'T a scam, and I'd be really careful and check out any place you're considering very thoroughly, because there are plenty of scams out there.
How it works with my company is this: The doctor calls the company's dictation line over the phone and dictates a report. The report is saved as a .wav and posted online, where the transcriptionist listens to it and types it up. When we're done, we upload our completed Word documents to the company's site, and then at some point they pay us for it.

(The company I work for has several different accounts at different hospitals etc, all of which work slightly differently, but this is the basic gist.)
The pay for an MT varies, starting at 5 or 6 cents a line and going up from there depending on your experience, aptitude, what kind of jobs you're doing, and for whom. The drawback I can see in your case is that you would need training before you could start. I took a $1000, six-month course before I started and then participated in a three-month unpaid internship to get my accuracy up to the point that the company could hire me (you're dealing with medical records, so you need to be accurate). I actually was hired before the three months was up, but it all depends on how you do. It's essential that you learn medical vocabulary and are able to understand various accents and ways of speaking--I swear, some doctors slur like they're completely drunk on a regular basis.
Also, with most companies you won't get hired as an employee, but a sub-contractor. That means they don't take money out of your paychecks for taxes, and you have to file as self-employed, which is a pain in the neck. But for me, being able to work at home and set my own hours is worth it.
Anyway, if you have any particular questions about MT, you can feel free to PM me.