The Swords & Wizardry Quick Start by Michael Shorten is an excellent introduction to Swords & Wizardry and serves well for any older editions of D&D. It also includes a small dungeon that can be used for a short adventure in any campaign. The Quick Start can be downloaded for free here. Plus you can purchase a hard copy here.
The key element of adapting the Quick Start Dungeon is that is the lair of a evil cleric worshiping a evil frog deity. She has skeleton minions making her a bit of a necromancer. In addition she obviously allied with a goblin tribe and to round out the dungeon denizens is Marcus the were-rat and his rat friends.
Finally there are some prisoners waiting to be rescued. You could plant NPCs here to fuel further plot. Perhaps one of the rescued fighters provide a way for the players to get into an important organization like a noble family, guild, or a law aligned temple. Certainly you could put an important local that was kidnapped. The player hired to rescue this person.
All of this can be tied to together to make the Quick-Start dungeon a nasty little lair of an evil cult. Another consideration is the magical mushrooms and the strange fountains. The evil clerics and her minions don't seem powerful or savvy enough to have actually created the place. So perhaps, like many dungeons, it was built in an earlier time. You expand on this idea to act as an initial seed for a larger plot in your campaign.
While simplistic I find these type of dungeons often the easiest to adapt. Utterly devoid of background this can be easily transformed into the type of locale you need for your campaign.