You should take a look at the MD/PhD forum, there is a lot of specific information on this.
But just to give you a general overview:
1) You NEED in depth research experience. This usually means not only having multiple years of lab experience, but taking point on your own project. Successful applicants have designed their own projects, conducted experiments for them, analyzed their data, written up their studies, presented their projects, etc...
2) You should have strong LORs from your research advisors (usually, 2 letters are required) in addition to letters from faculty. These letters give ADCOM members an idea of your scientific potential and are very important.
3) Other requirements are similar to MD-only programs. You should have a good GPA and strong MCAT, and at least a small bit of clinical experience (although this is much less important than it is for MD-only programs). Obviously, the higher your scores/stats are the better, but amazing research experience can usually overcome closer to average numbers (with the exception of some of the big name schools).
To answer your other question, coursework isn't usually the starting point for running your own project. Typically applicants begin by working or volunteering in a lab, and once they are trained in all of the lab's vital techniques and are familiar enough with the topics of research, they will ask to take on an independent project. Generally, you will need at least a year and a half to get significant results out of an independent project AFTER you have been offered one.
