It's certainly possible to study for and pass the exams through self-study. You can obtain your OCA that way. The pages linked below contain links to self-study materials for those three exams:
However, for the OCP, one hands-on course is required, so you must take at least one course to gain that OCP designation. The course does not necessarily have to be specifically directed towards one of the three tests. Several advanced courses are options for people who are already familiar with the information being tested. Most people, however, takes one of the courses specifically directed at preparing for on of the exams (generally 1Z0-053). The link below contains both links to the approved courses and to a page where you can search for authorized providers in your area. You can take the course before or after you pass the exams, but the OCP will not be awarded until you have taken the training *and* passed the exams.