How can a lay person approach the learning process of Buddhism?
There are many specific ways, giving you the best way requires a scientific study done on every possible way buddism can be taught and then finding a distinct right answer from that, which is currently, and probably never be available. I will give you a source that teaches you in a very specific and effect way of practicing buddism:

https://www.youtube.com/user/ActualizedOrg/videos

Specifically his meditation videos guide you through to enlightenment very effectively.