You need to make an appointment with an optometrist to ensure that you can wear contact lenses and to get fitted for lenses as well as pinpoint your contact lens prescription which is different from a glasses prescription. Lenses sit on your eyes, glasses sit a few centimeters in front of your eyes so the powers can vary between the two prescriptions.
From that point, you can either buy through the office or take your prescription and shop elsewhere. Where you shop is also dependent upon your actual prescription. Higher prescriptions and specialization generally require your lenses to be custom made, your optometrist can tell you more about it.
Also it will be beneficial if you check out the Contact Lens FAQ