I think most legit work from home jobs are the result of negotiating with your current employer the possibility of doing your current job from home, not so much a new legit work from home job.
You need at minimum a Masters degree and at least 18 graduate credits in the subject you wish to teach. Even then it can be hard to break into, because it's a good gig, although pay varies greatly. Took me almost a year from when I started applying to when I started my first class.
Re: Work from home
How do you go about getting started with this? Is a bachelors degree sufficient, or is a Masters needed?