For those students registering as a Category 3 for training on a/c with MCTOW of 12,500 lbs or less you may begin training as soon as the TSA acknowledges receipt of your fingerprint cards and any identity/citizenship documentation requested during your registration. You do not need to wait for approval from the TSA to begin training or take a checkride.
www.flightschoolcandidates.gov is the registration website and details the process on the frontpage.
Feel free to e-mail if you have any questions on the registration process itself.