Medical schools require that you take certain pre-medical classes as undergraduate.
In addition, many schools require a certain number of credits in non-science classes. Less common are the schools that have more specific requirements such as coursework in Behavioral Sciences (Psychology), Philosophy, etc. Consult particular medschools (or look at their web sites) to find out the specifics.
Pre-med requirements play a very important role in admissions for several reasons.
There is an obvious way to succeed in your premed classes: work hard, and this is obvious and true for all classes.
Yet science classes that make up the premed requirements are different from all others. For one, they are the lifeline to your medical career. They also require different approach than let's say History, Psychology or Anthropology.
In all your science premed classes: Freshman Chemistry, Organic Chemistry, Physics, Calculus and to some extend in Biology, the difference between a good grade and a bad grade is not necessarily knowing stuff. You can read Chemistry all you want and know every tiny fact about it but the chance is that this alone will not ensure you a good grade.
The "secret" to doing well in these classes is:
Withoug doing MANY practice problems you will NEVER do well on the exams. Most exams I've seen are structured to test problem-solving ability and this is also true of MCAT. So, do spend the extra time practicing solving actual problems. Get a solution manual for your textbook and check yourself.
For Organic Chemistry and Physics, you should be aware that often there are more than one correct way to solve a problem. The solution manual for your textbooks will usually give only one approach. You would know if you solved it correctly in Physics because if you did you will get the same numbers. In organic chemistry, there is no way for you to know for sure if your "alternative" solution is correct because even though you may have gotten the right result, your methods may be erroneous. I would recommend that you take your solution to your professors or TAs and ask them to look at it. You will derive two benefits from doing so: (1) you will know if you solved problems correctly, and more important, (2) if you did not solve it correctly, you will understand why your approach is erroneous and does not work.
I had trouble with organic chemistry and I have found a "miracle" book that helped me both to understand organic chemistry and to ace the second semester of it. The book is "Guidebook to Mechanisms in Organic Chemistry" by Peter Sykes. I think the book is excellent. It is a hybrid of a review book and a "guidebook" that explains the foundations of organic reactivity by type of reaction. I feel it is a valuable book. I found it very useful for reviewing for MCAT, which I took two years after I took Organic Chemistry. The book is pricey--so you may want to check your library.
I do not have any "useful" book suggestions for any other premed classes, so please do not ask.