Qualifications
A blastocyst culture, from which embryonic stem cells are taken, is usually between two days and five days old (source). About how much education will you need to be able to work with a blastocyst? A heck of a lot more than two to five days, that's for sure.
In addition to four years spent pursuing a bachelor's degree, you'll likely need a Ph.D. in a biological science such as microbiology. In the United States, a doctoral program often takes at least five years. If you graduate, then you're probably good at hitting the books and studying PowerPoint slide after PowerPoint slide—don't worry, though, that class on "responsible research conduct" will come in handy. But cell biologists need some life skills, too.
Fine, maybe not life skills. Just lab skills. Some techniques you just can't learn by reading about 'em. So take that teacher's assistantship, research fellowship, or internship job, and don't look back.
The hours are long and the pay is low, especially when you're first starting out, so you'll also need to be dead-sure you're motivated to do this kind of work. You need to be interested in cells at the most fundamental level. The structure of a cell needs to be the thing holding your attention, not the remote chance that you'll one day solve whatever particular disease your great-uncle suffered from.