One of the things I've discovered is that almost no one wants to do homework between games. Playing games is fun, and homework isn't. If it was, it would be called homefun (or maybe a 'game').
I used to try to assign my players homework, and it never went over well. It didn't matter if it involved reading world background, or writing up something for the world or the game. I rarely had anyone willing to do any outside reading or writing aside from maybe a brief character background.
Now I offer my players 150xp per character level to write up a summary of what happened in the game. I usually get one back, at least for my old school games.
As a DM, I've found that I also don't really want to do homework either, and the biggest pile of DMing homework is prep. There are a couple of ways to cut down on prep, aside from the “just wing it” school of gaming. While that's great for someone with fantastic improv skills, the rest of us we need a little more.
One strategy is to have a nice selection of random charts that you can roll on before hand or at the table. Depending on what type of game you're running will determine what type of charts you'll want. For a hex crawl, you'll want random encounter tables and a random hex table, and maybe a random weather generator. If you're running a random megadungeon crawl, you'll need some sort of dungeon generator, and again, encounter tables.
Another option is to grab a module that you've got kicking around, and running it cold, or nearly so. This works really well if it's one you've run before, but even if it's not, you can still do it. Just give it a read through, and then get to the table. If you mess something up, go with it. Let it be weird and fun and a little crazy.
The big thing though is to keep moving. Don't pause a lot, don't say "Oh I messed that up, there wasn't a trap there" after rolling damage. Guess what? There WAS a trap there, and it caused whatever damage you just rolled! Know why? Because you already said so, and you're the Dungeon Master! Keep the game moving. If your players are dithering, give them a random encounter roll.
Heck, just start rolling dice, and look like you're consulting the charts you brought with you.
Have someone kick in the door and start shooting. Have a peasant charge them with a pitchfork. Have the sheriff come to arrest them. Have a flying saucer crash! It may not make much sense. It might change whatever you were doing before. It will probably be one of the most memorable sessions you and your players will have together.
This post is both #9 and #10 of the 30 Days of Gamemastering Challenge