Prerequisite Classes: You will need to take the same basic prerequisite classes that most students need to get into medical school: 2 semesters each of biology, general chemistry, organic chemistry, and physics. In addition to these classes, upper level biology classes such as genetics, physiology, and biochemistry are usually strongly encouraged or required.
GPA: MD/PhD programs take the cream of the crop, and they can afford to be picky. A GPA of 3.8+ is great; a GPA below 3.6-3.7 will probably hurt your application. Showing a strong upward trend will help you, though (for example, if you got a 3.0 your freshman year but aced everything since then, you probably will do fine in the medical school admissions process.)
MCAT: MD/PhD programs have high standards for the MCAT, and usually MD/PhD applicants outscore regular medical school applicants significantly. Aim for a 35+, though you can probably apply with a reasonable chance of success with a 32+. This is not a place to scrimp and save money, because your GPA and your MCAT are your foot in the door - you will be screened out based on your numbers if they are not high enough. So take an MCAT prep course, buy MCAT prep books, get an MCAT tutor - do whatever you need to ace the MCAT.
Clinical Experience: This is very important for regular medical school admissions, though not as important for MD/PhD programs. You do need to have some clinical experience - usually in the form of shadowing doctors in a couple of different specialties or clinical volunteering. Probably about 50-100 hours of experience on your application should suffice, as long as you have seen enough of medicine to be able to talk about it at your interview.
Volunteering: This is very important for straight medical school applicants, but it can play a significant role in MD/PhD admissions too - particularly if you have volunteer experiences that are unusual or unique. You don't have to be involved in everything - pick two or three things that you are passionate about and put a lot of time into those activities. Admissions committees often look for evidence of commitment (how many years you have volunteered at a particular place) so make sure you have at least a couple of years of volunteering.
Research Experience: This is one of the most important parts of your application to an MD/PhD program. You need to have at least 2 years of research experience; 3 or more years is preferred. You do not have to have published papers, but you should try and present a poster or an abstract of your work at a conference - even an undergraduate research conference. You should be intellectually involved in your research and be able to talk about it intelligently at an interview.
Other Interests: This is a relatively neutral application criterion. If you have unique interests or talents, you can showcase them here, but you probably won't be penalized if you don't. This section really helped me get into an MD/PhD program; I talked about my hobby of jewelry designing and wore some of my pieces to every interview. At every single school I interviewed at, I was asked about my jewelry design and people commented on the pieces I was wearing.