In the book The Restaurant at the End of the Universe, it's very clearly explained how Zaphod gets into the simulated universe; he's in it from the moment he enters Zarniwop's office, and a big deal is made of him leaving via the window rather than the door so that he stays in it.
In the radio series, however, this doesn't happen. At the end of Fit the Seventh, Zaphod asks "How do we get to this universe, then?" and Roosta replies "I'm afraid it looks like we don't...", pointing out that the building is splitting down the middle, preventing them reaching the office.
Later, in Fit the Twelfth, Zaphod finally meets Zarniwoop in the lounge of the slightly-delayed spaceliner and reacts with astonishment at learning he's been in the artificial universe all this time. "How did we get into it? I mean like where, when?"
Zarniwoop only replies enigmatically: "You didn't notice? Well, I'll let you work it out for yourself."
So, how did he get in? As noted, he never actually entered Zarniwoop's office. My only thought is that it happened during the "body debit" incident with the disco, but there's no particular indication that that should be the case. Is there any other possibility?