It may seem kind of obvious, but Basic/Expert D&D is pretty much a no-prep game. Maybe not if it's your first time to tun or play, but assuming you have some experience then it really boils down to this:
- Grab the rulebook
- Grab an adventure
- Read said adventure
- Gather and roll!
For me and most of my players at this point in our gaming lives this is all it takes. Now we don't play it all that often because it's almost too simple, but that simplicity is exactly what makes this kind of no-notice run possible.
Even character creation is simple enough to be done at the table. In a few minutes the party is ready to go. Simpler characters also make it easy to run more than one character, which makes it even easier to get to actually playing the game as you could run with as few as two players.
It's priced nicely too. If you don't have a copy of the rules, well:
...and there are a bunch of others out there too, some more fiddly than others.
If you need an adventure then D&D Classics has a bunch of ...classics... for small prices and Dragonsfoot has a bunch of old-style but more recently created adventures for free.
Most of these kinds of adventures are not complicated so I wouldn't spend much time re-reading or re-working the module - just run it and enjoy! Most of them will take at least a few sessions to plow through so once you've started you are set for a while.
This is really the opposite end of the scale from my Pathfinder post. In that case technology and a certain approach let me run a complex game with very little preparation. In this case the game is simple enough and familiar enough that I don't need any technology to run it - just what's mentioned above and pencil/paper/dice. That's a great thing! No, it isn't a replacement for a game like Pathfinder for my players, but it's so easy to do that it makes for a fine game when you want one without a lot of rules or setting crunch and just want to get on with the adventure and play.