Take 290 HOV to the transit center, then go 610 South past the Galleria to 59 North, and take it to the Greenbriar exit. Exit right on Greenbriar, take it all the way to University by Rice Stadium, then turn left and you'll head straight to the Medical Center.
If you are not familiar with how to get out of the HOV at the transit center and get to the Loop (or I-10 if you take that way), better take a few looks at either Mapquest, Google Maps, or maybe the Houston Metro site. It's pretty easy once you have done it once.
If you have to go in rush hour, do not try to take 290 WITHOUT the HOV. It will take too freaking long most days to take the main lanes with all of the regular folks.
I've made many trips to Methodist in the last two years, and M.D. Anderson is just on the other side of Methodist.