The game starts with a notice: there you need to press either [D] or [N] (as indicated on screen).
After that, the intro will load automatically. At each screen of the intro, press [FIRE] when the green arrow flashes to pass to the next screen (or to start the game when the logo is displayed).
Once the game loads, it starts with the ApocalypShield interface getting corrupted (done intentionally done to represent the fact that somebody is hacking into it): that's where you enter your name.
After that, the interface is restored and you can start the game.
For more details, please check the file USEFUL_TIPS.txt and, even better, the on-disk manual (you can start this from the game's own menu).
Note about the loads: please be patient, the game runs precisely on the Commodore 64, so it takes a few seconds ;)