Determine if you want to take a genetics course for credit and at what level you are capable of studying. This will depend on your background in science.
Research available courses. Try MIT's free OpenCourseWare site, which offers both basic and more intensive levels of genetics courses. For a genetics course that will give you academic credit upon completion, you must enroll in an accredited online program, such as The Open University, which offers a Human Genetics and Health course.
Keep to a consistent schedule of studying for the course within the time frame allowed for the completion of the course, and submit homework assignments and exams as required by the instructor if you are taking a for-credit class.
Supplement your online study with genetics textbooks from a used bookstore or the library. There also are plenty of resources online you can use to explore current genetic research, which can help you get a better understanding of the real-world application of genetics.