Note: Most of the applications referenced below can be accessed from http://www.cmu.edu/hub
Registration can be a little intimidating at first, so hopefully this will answer some of the questions you have. I've tried to break it down into steps. Note that, if you are an incoming Freshman, you can safely ignore all of this. Your registration will either have been done for you or will be done during orientation.
Academic Audit - This lets you check your current credits versus graduation requirements for your major. This is useful as an initial check as to what you should be taking.
Schedule of Classes - This should be one of your first stops to see a listing of courses and picking out things that pique your interest.
Scheduleman - A tool provided by the Tartan that lets you manipulate your schedule in real time and share it with others. Probably the most popular right now to use for preliminary schedulewanking.
TCPulse Scheduler - Another tool used for schedulewanking. This does not require you to register to be able to share schedules, but it usually does require you to basically have a schedule planned out beforehand. This is probably most useful if you simply want to display your schedule in a graphic form.
CIO - Course Information Online is useful for you to check waitlist statuses on courses, as well as seeing availability for you personally, taking class reservations into account. This should be used liberally to ensure you're not banking on a course that filled up days before your registration time.
FCEs - You can read previous faculty course evaluations here. It's not much use as far as finding courses goes (since you'll usually take courses based on what you need rather than on the professor teaching it), but it can help you make a decision to postpone the class another semester or so if the professor next semester sucks.
OLR - This is where you actually register your classes.