Go to college and choose a major with research topics that are interesting. The major itself does not matter too much, although some majors might be more suited for continued research than others. See Resources for a description of the common majors offered by American universities and for a ranking of American and world universities.
Seek undergraduate research experience during the school year. Speak with an adviser in the department to ask about undergraduate research programs offered by the department. Most science and engineering departments in universities offer some sort of funded undergraduate research program where a student can work alongside a professor and his research assistants and students in leading edge research.
If such a program is not available, speak directly with professors and inquire about their research and whether or not they would accept help in their laboratories. This route is mostly unpaid, but it is the experience that matters.
Seek research experience for undergraduates (REUs) during the summer months. REUs are summer research programs sponsored by the National Science Foundation to engage undergraduate students in research. REUs are paid and take place in many universities around the world. REUs also offer free housing and food allocations for students. REUs are a great way to live in another part of the country or the world for the summer and to gain valuable research experience as an undergraduate.
Attend graduate school for a master's degree or doctoral degree to continue conducting research. Having undergraduate research experience is important because graduate school is based heavily on conducting research. A master's degree typically requires a thesis to be written and a public defense of the thesis, and a doctoral degree requires contribution to a previously unknown or unexplored sector in one's particular field of research.