Then go to the library and read those people's papers. Try to focus on more than one potential advisor, to keep your options open. First, past research experience is an important indicator of a student's maturity and the ability to get involved in future research. Finally, conducting research in someone's lab allows you to get a really strong and detailed letter of reference from a professor who knows you well. The best research experience would be work that leads to a publication with you being one of the authors.
Every graduate program gets far more applicants than can be trained.
If the person has room and is sufficiently impressed with you, he or she will go to bat for you with the Graduate Admissions committee. Strong advocacy from a respected faculty member can lift an otherwise average applicant to the top of the heap. Most graduate programs have one deadline a year, and it is often in January. If you want to enter graduate school the following fall or spring, you must meet the deadline. If you miss it, your file will either be tossed out or languish for a year.