The task of becoming a diagnostic radiologist is not an easy one. Radiology is a competitive field. Each year, hundreds of applicants from within the United States as well as international medical graduates apply for approximately 900 residency training spots in roughly 100 programs located across the United States. While not as competitive as other residencies such as dermatology or radiation oncology, the field is definitely above average within the medical specialties. Even after a resident matches, they face another 5 to 6 years of intense training as well as two major exams before even their first day practicing as a diagnostic radiologist. If you are determined to become a radiologist, you must be willing to make this kind of commitment.
To learn more, check out How To Become A Radiologist. Other good resources include Aunt Minnie (a website and forum dedicated to radiology) as well as the Wikipedia article on Radiology.