To reiterate three very good points above. Always use reaction rolls, always use morale rolls, and always use wandering monsters (not just in the dungeons). For basically the reasons stated above. But they also apply to overland travel as well. If the players want their character to reach the dungeon or adventure sight as well-rested as possible, they will actively avoid pointless combats along the way, but they will have plenty of opportunity to role-play, fight, and explore if they want to before reaching the dungeon.
It might help to pass around the Principia Apochrypha.
Principia Apocrypha is a new, free Primer for OSR and other Old School Style RPG Gaming in the form of a collection of Apocalypse World-s...
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My points would be.
1. Don't house rule until you've given the game as written a fair shake. Create characters as per the rules. Follow the procedures of play. Roll some checks for the players when their characters wouldn't know the outcome either way (secret doors, traps, etc). While not as tightly wound as modern games, the designers did know what they were doing and elements will interact with each other in unforeseen ways. Get used to the game first, then if you feel you need to make changes, hack away.
2. Follow the procedures of play. Roll to get lost. Roll to forage. If the party wants to hunt for food, they stop traveling to hunt. Players declare their actions at the start of the round. Casters can either move or cast spells. The procedures are there to both show you how the game is supposed to be played, but also to minimize adversarial refereeing. You're not deciding to put monsters in their path when they're already near dead, it's been an hour and the PCs are making noise, so it's time for a wandering monster check. It's not you deciding that a warband of 37 orcs happens to be on patrol, it's the dice making that determination. As such the world is dangerous and if the players want their PCs to survive, they have to play smart.
3. Keep track of time and resources. Older D&D games are very much resource management games. Time, food, water, spells, torches, oil, hit points, weight carried, etc are all resources to keep track of. It can be a lot at first. But it's worthwhile as it leads inevitably to hard choices. How long do you push in the dungeon with dwindling supplies? How much treasure do you pack out considering you still need to carry your arms and armor, food and water, etc? Do you toss food at chasing monsters in the hopes they're hungry and will leave you alone? These are the kinds of hard choices that make these games so interesting.
4. As often as possible, roll in the open. Some checks you'll need to keep behind the screen to avoid meta-gaming (secret doors, etc) but as much as you can, roll where the players can see. This avoids even the hint of adversarial refereeing. Wandering monsters, roll in the open. What the monsters are, roll in the open. Number appearing, roll in the open. Attacks and damage, in the open. Etc. You're not out to get the PCs or the players, you're following the dice.
5. Encourage the players' creativity. The biggest draw, for me, for older games is they are so light on rules and so deadly that they practically beg the players to get creative. So not only "let" the players get creative, but actively encourage it. More often than not, the players being creative will get them out of far more problems than combat or rolling dice will. Keep things grounded in the world you're using, but if some wild idea could work, give them a fair shot at it working. Description should always beat rolling dice.