How do I register my dogs with AKC so they can officially participate and earn points toward titles?

A good question!  There are three types of registrations you can use, depending on your dogs pedigree.
For registering a purebred dog for which you have all the necessary documentation, you'll want to visit AKC's registration page for purebred dogs and enter the required information.
For registering a dog that's a purebred, but you don't have the necessary documentation, you'll want to visit AKC's registration page for Purebred Alternative Listings and enter the required information.
For registering a dog that's not a purebred, or one that you just don't know what it's breed is, you'll want to visit AKC's registration page for their Canine Partners Program and enter the required information.
* - Remember to do any of these prior to attempting to register for any actual Fast CAT events.  A valid and unique registration number is required to enter events and AKC needs time to process the registration requests.  The length of time will depend on which registration type is chosen and how many requests AKC already has in their sytem.