I wrote this reply offline , so forgive me if the following has already been said. Much of my advice is edition-neutral, and reflect my views on old school gaming – others will probably disagree with some or all of my points. So there.
1. Restrictions, not options: 3e is designed to allow PCs to create any PC they could dream of, and provides several tools for such customization. PCs are often constructed to reflect a character coming from a specific and highly individualized pre-written backstory. In old school games, character choice is based on dice rolls, and the player has to build a character on his or her “god-given” abilities (as per the 1e PHB, p. 7.). Encourage character creation to be quick, focusing on a restricted array of races and classes, and work out details as play progresses. PCs should start as a “blank slate” and develop a background and personality through the events of the campaign. It might be a good idea to use 4d6 in order for stat generation (or two such arrays if you are generous), and restrict runaway multiclassing with a strict XP penalty. Actually, you should encourage the players to play single-class characters. Don’t allow prestige classes or extra-PHB feats and skills. Don't allow sorcerers either.
2. Nature versus Nurture: old school games are strongly Darwinian. The lucky and the shrewd survive and become stronger, the weak and foolish perish. Do not populate the world with “appropriate challenges”. Populate the world with a lot of random, cool stuff. That doesn’t mean you should put undetectable deathtraps in a starter dungeon, but if the PCs disregard ominous clues, they should “suffer greatly”™. For example, if they venture too deep into a dungeon, it is fair to let them encounter a basilisk or a young dragon, or a higher level Wizard, NO MATTER how high level they are. In such situations, cunning or a speedy retreat may still prevail, but there is a good chance PCs will die, often in great numbers. So be it, dying is fun and makes fun war stories later on. At the low levels, it is perfectly normal if PC turnover is high, with casualties every session or so. Getting and playing a PC to higher levels becomes more of a reward if it is not guaranteed. Thus, do not fudge, do not hold back the fury of Hell (extreme cases notwithstanding).
3. Slow character progression. Necromancer Games developed an alternate XP table where the XP goals for each level are doubled, e.g. 2000 XP for level two, 2000+4000=6000 for level three, 6000+6000=12000 for level four, etc. In my experience with my 3.0 campaigns, the formula works pretty neatly, especially coupled with the aforementioned attrition factor.
4. Blatant materialism: PCs should be fortune-seekers out for adventure and wealth. Avoid grand quests, especially until the PCs reach high levels (that’s 9th and up in old school games, BTW). Focus on greed, power acquisition and even extreme selfishness. Let the world be a foe itself, an impersonal and materialistic entity that seeks the PCs’ downfall. Adapt a somewhat antagonistic attitude (but still play fair). Even gods should be anthropomorphic and predictably egoistic instead of inscrutable and based on abstract human ideals. They are, after all, merely very high level characters, who may be more powerful than you, but possess the same character flaws. [Note: many 1e campaigns used a more idealistic worldview, but I have found that this approach can make for a very fun old school experience.]
5. Chaos and unpredictability: don’t let the campaign fall into standard tropes. Do not aim to create a realistic feudal society, or even a too coherent setting. Focus on dreaming up crazed and improbable worlds where death and glory avaits in every corner of the world, from islands inhabited by crazed amazon queens to glaciers where frost-worms and ice demons dwell. When creating dungeons, feel free to disregard ecologies. A room with a cool trap is old school (and so are dungeons with extensive sub-levels, multiple connections and a ton of hidden areas), the tenth armory and barracks is not. Unexplained weirdness is old school as well (“What is that great stone head doing in the dungeon room?” “Why does that fountain generate an infinite number of skeletons?” “Who is the oracle of Blackstone Mountain?”). Let the PCs wonder and make up their own explanations.
6. Challenge the players, not the PCs: do not distill most challenges to a skill check. Everyone can roll dice, and it is fun, but too much of it can become boring. Create challenges where player judgement is the primary factor of the outcome (sometimes with a generous helping of pure chance). If you can get away with it, do away with all social skills such as Diplomacy and Bluff.
7. Stories are secondary, gaming is paramount: do not pre-plot adventures. It is fine to have an initial premise, but try to create settings, focusing on places the party can visit, and let them explore this environment as they wish. Give them a lot of self-contained side-areas to explore and experience (an abandoned tower, an island near the seacoast, a mountain renowned for its enchanted statues, etc.). Keep the action moving and prepare for a lot of improvisation. Exploring the wilderness and dungeons is just as fun as going on a quest. For some of us, it is more fun, even!
8. Monster and treasure selection: it is my experience that conservative monster and treasure selection is one of the key factors in the success of old school play. If you have the 1e Monster Manual I, you have a good baseline with enough “basic” monsters and weirdness to sustain most of a campaign. You don’t need more variety than that. Of course, feel free to create an advanced specimen or two (an orc chieftain who is a 6th level Fighter, or a giant lizard that has a fiery breath), but try to rely on what the book gives you. Don’t do too many templates. Lich and vampire are pretty much the only worthwhile ones in the 3e MM (maybe ghost as well); the rest is filler. Avoid two many spiky things or übermonsters. A horde of weak opponents is just as good as a “Big Bad”, and there is nothing like killing enemies by the dozens. A 6th level party
can defeat 60-80 gnolls, maybe even more: that’s very 1e, too. The same goes for treasures. Some items feel very old school: +1 swords, potions of healing, wands of frost and horns of Valhalla. That sort of stuff.
9. Simple opponents: you do not have to – indeed, you should
not – create highly specific opponents for your PCs. A half-fiend necromancer is superfluous and even silly. A 7th level human Wizard who can cast fireballs is enough. A beholder is enough. Five evil fighters and an evil cleric are enough. A half-orc assassin (the nonmagical type, such as a 7th level rogue) is enough. All of these are sufficient for an exciting campaign. Don’t overdo it. In fact, a certain simplicity is a benefit for old school campaigns.
10. 10th level is high level. In traditional AD&D, 1st to 4th level could be considered low level, 5th to 8th mid-level and anything above that high level. A 10th level PC is already a great hero – a Lord, a High Priest, a Master Wizard or a Master Thief (again, as per the level titles in the 1e PHB). If the PCs have achieved that level, it is time for them to go into semi-retirement. There is a good reason for slow advancement, because the adventurers aren’t supposed to really reach those very high levels. If you can cast Raise Dead, Teleport and the like, you are already at the top of the heap. Accordingly, most NPCs should obey the same rules. If the master of a city is a 7th level Thief, that’s good enough. Added bonus: in this environment, PCs can more easily become people of note.
+1. Do not be apologetic. Old school does not have to be a guilty pleasure, but many people treat it that way. Avoid this pitfall. Old school gaming is fun, AD&Dism have an important role in the feel of the game, and to Hell with those who would deny their greatness. There is nothing wrong with memorization, there is nothing wrong with strictly defined and restrictive classes, there is nothing wrong with dungeons or unplotted campaigns. Not at all – all of these are a lot of fun, and they should be embraced and understood instead of rejected as “bad game design” or “nostalgic appeal”.
Following the above advice (or some of it), you can run a meaningful old school campaign. I did so for about four years – eventually switched to Castles and Crusades, but I do not think my experiences with 3e were bad or anything, or that it is impossible to use 3e to run an old school game. But you have to be firm in some areas, and be prepared to make a few hard choices, including cutting back player freedoms and perks 3e tends to dole out a bit too frequently. That, in my opinion, is the hardest part of it all. If you have a party who understands your aims and cooperates, you won’t have too many problems. Otherwise, it will be an uphill battle.