Do you want to run an original-style campaign? Here's my advice. This is one man's opinion, perhaps given a little extra weight by the fact this is how I did it in 1975 and it worked for me. This is, by no means, the only way to run an OD&D campaign.
Get a copy of OD&D. The books are available second-hand from a variety of sources, including eBay and used bookstores. New rules sets are still legally available as a reprinted Anniversary Boxed set from Hasbro.
Why not a clone? Emulations of the OD&D rules, called clones or retroclones, are great games and there are good ones available. As good as they are, however, they are still someone's interpretation of the OD&D rules. The reason why this is so should become apparent to the discerning reader after perusing the original booklets. Since the originals are still available, why not go straight to the source if recreating a 1970's experience is your goal?
Don't overthink it! It's a game, written and published by amateurs. Experienced gamers and very intelligent persons, certainly, but still publishing amateurs. I've seen folks dissecting the written text with the fervor of a Bible scholar but the text very often means what the common sense interpretation of the wording says it means. Be wary of the phrase "could be taken to mean" during rules discussions. What follows will likely be a tortured interpretation of a fairly straightforward but poorly worded sentence.
You don't need anything else. There are folks swearing to hell and gone you need "x" to play the game, where x = some other work or reference. You really don't, what you need is imagination. Most commonly cited as "must haves" are the Chainmail rules for miniature warfare and Outdoor Survival board game by Avalon Hill. There are references to both in the OD&D rules but most everything you need from either is repeated in the text or easily done without. If you have them and want to use them? Great! They'll certainly be useful but they are not necessary to your game.
It's all compatible. There are a lot of published works specifically intended for use with OD&D. The various published supplements, material from The Strategic Review and The Dragon magazines, fan work on the internet, published modules, et al. Casting an even wider net? Pretty much anything published for any pre-1983 D&D rules set can be used "as is" or with little modification with OD&D. Going even wider, most FRPG supplements and rules can be adapted to the game. Go wild.
Make a ruling and run with it. There are ambiguities and omissions in the rules. Don't get all in a lather trying to find an "official" word. As referee, decide how it should work and note your ruling for future reference. If it doesn't work well in play, modify or change it as needed until it's a good fit.
Be prepared. Your players will often do the unexpected. The best way to handle this is to prepare extra material that can be plugged into the session with little trouble. Goblin camps, smaller dungeons of 1-3 levels to serve as the objects of map-based quests or teleport curses, shops, small castles, houses, lists of NPC names, a small stack of NPC character sheets ... all these things will help you "wing it." If all else fails, simply admit to the players you need time to prepare for this latest twist and adjourn the gaming session for the evening.
Borrow. Take inspiration from other rules sets, published adventurers, books, and films. Is there an aspect of a treasured piece of literature you enjoy? The hurtloam of Illearth, for example, sequins from Tschai, the Force from Star Wars, radium pistols from Barsoom, and so on; all can be put into your game if you so desire. Adapt it, try it out, leave it as is or alter to taste. Don't be afraid to tell your players these items are in on a trial basis.
Excise. Don't like the Cleric class (for example) as written? Delete it. Just as you shouldn't be afraid to put something in, don't stress about removing rules. A lot of great fantasy literature revolves around only fighters, or wizards, or wily thieves, so do you really need the other classes? Your choice.
Start small, go big. You don't need a fully realized and fleshed out world to begin a campaign. You need a good general idea of how the world works and what the surrounding region is like but you don't need a lot of detail. Map out the starting hex containing the player-character's base of operations, usually a village or town, and nearby locations of note. These will include humanoid lairs, monsters, dungeons, and other friendly settlements.