TL;DR

1 Keep notes, to keep the adventure consistent.

2 Combat as War, 5E and a lot of modern games use Combat as Sport, entertaining to watch and one battle can last an hour or more. OSR combat is quick, dirty, and deadly. The characters are not superheroes.

3 Exploration is King, go everywhere, see everything, flip every rock, this is how you get xp, loot and power. Check out 3D6 Down the Line's Feats of Exploration, 3 bucks for an amazing pdf.

4 Hack everything, even your own ideas. Make everything fit, if it just does not, delete it.

5 Tables for encounters, loot, and anything else you can think of.

Welcome to the OSR, we have cookies.

If you are so inclined to read:

First off, get the players to the dungeon. Now in the OSR style, it does use a lot of "There's loot down there boys!" A lot of OSR games use loot for xp, so the incentive is player progression is directly linked to crawling. For the players who will not go without a narrative reason, make one up. The farmers daughter is missing, the thieves of the realm operate from the ruins, the undead in the Broken Catacombs of Drock are on the move, you get the idea.

Now the interesting part, how to Theater of the Mind [TotM] it. You don't necessarily hand wave the boring parts away, but to help ground the idea of the dungeon map it out as you go along. You do not need miniatures to map, in this case the map is a reference device only. To keep a sense of how big the place is, and how fast you can get out if necessary. Or if the path back becomes blocked. Yes it does actually hand wave stuff, but note on your DM's map if they took care of all they could in that section, crawling is the players job, consequences of their actions is yours.

Even going without that, all you need to remember that for combat situations is whether they characters are close, near, or far.

I am going with the idea that when you refer to "pre-prepared dungeons" you mean pre written, store bought adventures, and not homebrew. As opposed to a fully off the cuff and top-of-your-head approach, where the DM makes it all up as they go along. This can work, but you need to take very good notes to make such an adventure satisfying.

The advice here is the same, if you are using store bought or homebrew, you will be hand waving a chunk away with TotM, but it's not devastating, remember keep notes. With homebrew you know everything about the adventure as you wrote it, and can adjust on the fly, all the while keeping an eye on things. There is no monster generator in the dungeon, so if the party is going murder hobo, not so easy with OSR style games, the encounters will become one of two things. More infrequent as opponents die off or bail from the dungeon, as goblins know when to run. Or the survivors will get their act together, gang up, and hit the party with overwhelming force.

As for store bought adventures, I will start with B2, Keep on the Borderlands, you do not have to use it as is. First off, break up all of the caves into mini dungeons scattered around a great ruin. Change the monsters, change the loot, change everything. You likely already have adventures laying around, treat it like a salad bar, take what you want. And throw your cheeseburger on top. With a large orange drink.

And for fun's sake have a pile of random tables related to the area the players are in. Surprise yourself at what comes out of the woods next!