The above comment is a good overview. I'd add a couple things. #1) I don't think you have to major in sciences. Many schools actually like a candidate who has majored in something other than biology or chemistry as they see so many of those applicants. Major in something you like and that could also be useful should you not gain entry to medical school. Good GPA in college and doing well on the MCAT test won't necessarily get you into a school, but poor marks in either will keep you out. Med schools like candidates who have also demonstrated volunteer efforts, have some shadowing experience or have worked in some kind of medical field. Some schools even want to see that you've completed at least a year of language training. Once you get in college and closer to applying, you can get more information about what requirements schools have that you are interested in attending.
One mistake I see people make is applying to too few schools. While it is expensy, you should be willing to go anywhere in the country, so apply broadly.
Once in med school, there are more grades and standardized exams that you may have to do really well on depending on your desired specialty (high scores required for things like dermatology, Opthalmology, orthopedic surgery, and others). Another round of applications and then you do residency, which is kind of like an apprenticeship and school at the same time. Once residency is finished, many choose to do additional subspecialty training called fellowship. Once training is complete, there are standardized exams for each specialty.