I'm currently a third year grad student in neuroscience. I have a BS in Psychology and I spent 2.5 years working in a behavioral neuroscience lab on my undergraduate campus.
I believe the single most important thing you can do if your goal is to do neuroscience research is to work/volunteer in a lab (or labs!) as an undergrad. At the least you'll learn what it's really like to do research and at the most you have relevant experience under your belt and the potential to publish something. If your school doesn't have a neuroscience research program, find the most closely related biology or psychology labs to work in.

It depends on your school. Some colleges offer excellent undergrad level neuroscience degrees but since it's a newer field it tends to be more prominent in graduate school programs. If your school doesn't offer a dedicated neuroscience department or branch within the biology or psychology departments then you have some more work to do:

First prepare a basic science core. 1 semester of General Chem, 1 semester of Organic Chem, 2 semesters of physics (mechanics and electromagnetism), and at least 1 semester of basic biology. You should definitely take more biology though, especially human physiology, endocrinology, psycho biology and/or neurobiology. It's very important to take a statistics class and have at least single variable calculus down. Throw in some critical reading courses and make sure your science classes are lab classes.

Now you have a strong science core that leans towards neuroscientific study. These courses will help acclimate you to the scientific community, methods, and tools at your disposal. It's a wonderful community and if you love it you could add much to mankind's knowledge of the brain and further the well-being of humans.

Once you have this core planned out, remember to enjoy yourself as well. Take classes you have other interests in as well. One of the most famous neuroscientists today, Sam Harris, started out as a Philosophy major. Neuroscience is a very interdisciplinary study and knowledge of things like philosophy, psychology, music, art, sociology, and so on can be very helpful in broadening your view of cognitive and neuroscience.

There are quite a few tracks to go down when studying the brain. You may focus more on the chemistry and biology of the brain itself. You would be studying the exact mechanisms of how neurons talk to each other and how information is relayed, inhibited, or amplified. This field is very important and you may be able to produce research on cures for many neurological diseases that harm humans today (think MS, ALS, brain tumors, many viral diseases, and so on). In that case biochemistry and more organic chemistry will help you greatly. Computational biology will also be of great use. If you are more interested in higher cognitive processes, the line between neuroscience and psychology you may be more interested in cognitive science or "cognitive neuroscience." This is a track for people interested in the physical processes that form things like learning and memory and how they function and develop. Of course you will have much overlap with the more chemical side as well.

Many people who go into neuroscience at the graduate school level are psychology, biology, or chemistry majors that want to refine their knowledge into the more specific field of neuroscience.

No matter which track you go you must and will become familiar with the scientific method and good experiment practices. This is a growing field and well formed and carried out experiments are central to it. There are many mysteries to the brain and the world needs more neuroscientists to help address the holes in our knowledge about the brain and about the many diseases that can riddle it. Who knows your contribution to neuroscience may help end the plague that is Alzheimer's disease.

Edit: I'm currently a neuroscience major at a university well known for it's undergrad and graduate neuroscience programs.

The most important thing to do is to work in a neuro lab and try to get a paper. You are a freshman so you should be able to do it by your senior year. See what research is being done at your school, decided what you like best, then email that professor and tell them how cool their research is to fluff their ego. They like freshmen coming in as it's more likely they want something other than just a letter of rec.

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Along with what others have suggested, I think it is important to have a good understanding of statistics. Regardless of the kind of neuroscience you want to do, being able to interpret, digest, and critique statistical methods in neuroscience is invaluable. Not to mention, I believe stats will only become more important as time goes on (especially in computational, cognitive, and behavioral neuroscience.)