Typically the PVVET will submit its session electronically after the examination. Upon VEC (Laurel) approval, the information will be sent to the FCC (electronically) for processing.  This process can take a few hours up to a couple days depending on when the exam was administered (weekend applications will not be processed until the following Monday). This is assuming the FCC's EBF is up and running.
Those who are already licensed and have upgraded at the exam, soon as application is processed by the FCC, you should see it updated so you no longer have to use /AG or /AE after your call.
For those who are obtaining a new license (didn't have a license prior to the exam), you'll receive an e-mail from the FCC about the $35 application fee that must be paid to the FCC within 10 days. You should have been provided with instructions prior to leaving the exam.
Once your callsign appears in the FCC's ULS, you are legally allowed to use it on the air.
It's strongly suggested that you print and sign at least 2 copies of your license. If you wish to upgrade, you must bring a signed copy of your license that will be given to the team.