The main text of Gamma World concludes with an example of play -- one of my favorite parts of the rulebook. This example starts with world design, following a hypothetical referee (named Omar, which I thought odd at the time) as he prepares his campaign map. I've reproduced it below, because I think the map is quite interesting.
The rulebook stresses that the referee should not only know in advance just what might be found in all the important hexes but that he should also, when necessary, have sub-maps pertaining to them. The military base in the northwest quadrant of the map, for example, is given a map in the rulebook, since it's likely to be an early site for exploration by the PCs. Areas farther afield can be mapper and detailed later, but they should be detailed, since a key feature of a Gamma World campaign is its wide open nature. The PCs can, literally, go wherever they want across the ruined continent of North America, so the referee needs to be ready for every contingency.
A section on "Starting the Campaign" firmly establishes the idea that the PCs are inexperienced youths hoping to earn recognition as adults by leaving their primitive village to explore a nearby ruin of the Ancients. I won't say that every Gamma World campaign I've ever seen has used this set-up, but a great many of them have. In my experience, this is the default position that most players have come to expect, much in the same way that the default position of a beginning D&D campaign is that the PCs are inexperienced would-be adventurers seeking to prove their mettle by exploring a nearby underworld. I've often toyed with other starts to a Gamma World campaign, such as the PCs being part of a society that's managed to retain some higher technology, but I've never actually done so.
Like many old school rulebooks, Gamma World provides us with a transcript of play involving five PCs and the referee. That in itself is noteworthy, since it suggests that, even by 1978, the typical number of players had shrunk considerably since the early days of the hobby. Nevertheless, that party of five still has a "caller" who acts as the go-between for the players as they interact with the referee. There is no separate "mapper," this being part of the caller's job, though it's noted that the two roles could have been split. Precise mapping of the adventure locale seems important, with some of the initial dialog spent on getting the measurements of the rooms and corridors correct. Likewise, the players are paranoid, posting guards outside rooms and making clear to the referee that they're merely looking at but not touching things that they find.
The remainder of the dialog consists of the players discovering and learning how to operate a laser pistol and accidentally setting off an alarm that has alerted the robotoids of the ruin that someone has breached its defenses. There is no combat or use of mutations; indeed, it's unclear how many, if any, of the PCs are mutants of any sort. Compared to the examples of play shown in, say, the Holmes or Moldvay rulebooks, it's fairly unexciting, though it does teach the need for care when exploring a ruin of the Ancients.