You join a program simply by enrolling in any course that is part of that program -- there's no application.
After you enroll in a course that is part of a program credential, that program on your Programs dashboard here: https://courses.edx.org/dashboard/programs/
Click the name of any program for more details and the option to Enroll Now in any related courses, or upgrade all remaining courses.
To complete a program you must earn a verified certificate in each of the individual courses. After you earn a verified certificate in each course, you automatically receive your program certificate.
For additional information, see How do I take all the courses in a program?