You register for courses you're going to be examined on on LSE For You. Go to Student > Selection of Courses.
Moodle is a system where courses can post resources, such as lecture slides, handouts, extra readings, homeworks and quizzes. Enrolling on Moodle courses does not, as it says on the confirm screen, register you for the course. Sign up for your compulsory ones, and any options you are thinking of taking (to see if the content looks interesting, hard, etc...).
Some courses prefer to stay in the dark ages and frustratingly use the Exchange server's Public Folders to post all their stuff.
When I say course it means module.