According to the regs, you can mark yourself "Present?" at anytime "within" 24 hours (some terminals that offer Virtual Roll Calls are 20 hours) prior to a Space-A Roll Call. The time you get marked "Present" is not a factor in the Space-A selection process so around an hour prior to Roll Call is usually sufficient time to get settled before a Roll Call. To mark yourself "Present" you need to arrive at the terminal with all travel documents (including your passengers) and proceed to the Passenger Service Desk and they will mark you "present." Once marked "Present" you'll be added to the Present List and then can compete for seats at the Space-A Roll Call for flights heading to your desired destination. If unsuccessful and your name falls off the "Present" List you'll need to get marked "present" again. Some locations purge their "Present" List at midnight so make sure you inquire about their local policy.
NOTE: November 2016: AMC no longer allows passengers to mark themselves "Present" remotely The test locations were Kadena, Charleston, McGuire, Spangdahlem, and Ramstein. Virtual Roll Call is still available at certain locations.