I used to do medical transcription.
The first thing you need is an education in medical transcription. There are 3 schools typically recommended:
http://www.andrewsschool.com/
http://www.mtecinc.com/
http://www.careerstep.com/
Some people don't like Career Step as well as the others, but they cost less and people do get jobs after graduating from their program, so I still include them when I talk about it.
The pay depends on your productivity. I started out at $0.065 per 65 character line. My early days I earned less than minimum wage, but as my speed improved, and I eventually got a raise to $0.07/65 character line, I could earn up to $15/hour. Pay rates do go higher if you stick with it and are really good at it. My sister, who also transcribed, sometimes hit an average of $20/hour.
The work can be tough sometimes. Some doctors talk as though they don't realize someone has to understand them. Kind of like their reputation with handwriting. Others talk wonderfully clearly, and are a real delight to transcribe for.
One of the big benefits for me was that I could work my preferred hours, although I did have to set up my schedule in advance. That made it hard to work during naps, since those can vary a little, but easy to schedule myself to work after the kids were in bed.
If you have more questions, let me know, and I'll answer to the best of my ability.