This is a thing that has been going around Google+, a kind of survival guide for old school games, written by Ben Lehman. I'm sure everyone's seen it, but I wanted to post it...just in case:
Playing D&D is a skill. If you are not good at the necessary skills, the game will punish you by killing your characters. What I can do here is point you in the direction of what skilled play looks like. That isn't the same thing as teaching those skills, for which we would actually have to play the game together, but it can hopefully give you ideas about what to try.
My assumption in this piece is that the biggest stumbling block to D&D is the combat, rather than traps or mapping or so on. Obviously, there is different advice for different problems. But I have noticed that combat is the problem that 90% of modern gamers have with playing D&D.
The combat system of D&D is a punishment mechanic, not a reward mechanic. You do not want to get into a fight. Particularly as a 1st level character, fights will kill you dead. Every single attack roll has a fairly decent chance of killing you. Thus, you want to avoid being subject to attack rolls, by whatever means.
If you look at the D&D reward mechanic (experience points and treasure) this is obvious. You can orders of magnitude more experience points from treasure collection than you do from combat (monster killing). XP from combat plays basically no role in advancement whatsoever. Your approach to a dungeon should thus be surgical, rather than exhaustive: get in, get as much treasure as you can, and get out. You do not have to confront the dungeon on its own terms and, indeed, doing so will kill you.
As a player of modern (tabletop or video) games, this can be a hard adaptation to make. You have been trained through long experience to "clean out" dungeons and to treat combat as a resource expenditure (spend some hit points to pass the monster) rather than an out-and-out losing condition. However, D&D is not a game of resource management nearly as much as it is a game of creativity. Creatively navigating your environment is the only possible key to success.
There are a number of implications from the two core principles. I'll go over a few of my favorites.
Establish the Fiction The DM will naturally keep her descriptions fairly vague and nebulous, both because this is easier and it is of course clear in her head. Do not let her get away with this. Ask questions about your character's environment, about the exact spacing, about the exact locations. This is useful for two reasons: one, it will reveal potential resources and opportunities, and two if combat breaks out it will give your the proper spacing.
Jam Today is better than Jam Tomorrow. Listen up wizards. You've got your one sleep spell, and god-damn it you're going to save it because without it you're useless. So you hang on and then, bam, stray arrow gets you. You have made the classic error of delaying your gratification. Do not do this. Use whatever resources you have at your disposal right now before you're too dead to use them at all. If you run out of resources, retreat and regroup ASAP. You will not get through the early levels of D&D by being parsimonious with your victories.
Talk, Run, and Wait When you encounter a monster, you have four options: Fight, Talk, Run and Wait. This is not for show. This is the game giving you a last chance to avoid doing something stupid. If you have any possibility of avoiding combat with the non "fight" options, do it. This means, yes, you should pay attention to what languages your character speaks, as well as the internal politics (if any) of the dungeon. A character-killing fight could turn into an opportunity or a reward.
Prefer Cleverness to Arrows, Arrows to Swords If you can find a way to avoid a fight, do it. Light a bonfire and smoke out the goblins. Don't molest the Flesh Golem in the attic. Roll a boulder in front of the cave mouth and keep moving. However, if a fight is a must, try to engage on your terms: i.e. at range. Most early D&D monsters don't have ranged attacks, so engaging at range will give you a huge advantage. Note that bow ranges are much larger than the movement rate of most early monsters, so don't let the DM get away with "just one round of arrow fire then they close." Consult the rules, and keep in mind to establish the fiction.
Use your equipment, use the environment More than just a ten foot pole, everything on the equipment list is insanely valuable for navigating the dungeon. Get lots of oil and set things on fire, for instance, or use a mirror on a pole to look around corners. Anything in the dungeon, up to and including the walls, can be leveraged for your advantage.
Take your time Do not hastily move through the dungeon. As much as possible, take your time, secure retreat routes, and don't let the DM rattle you. Remember: there is always another dungeon. Don't take risks that aren't both calculated and absolutely necessary.
I feel like there's a huge culture shock being exposed to D&D for the first time. A lot of video gamers, Forgies / Story Gamers, and players of modern forms of D&D are used to the game's mechanics being their friends, to being able to leave the fiction in a muddled cloud, and to not having to actually struggle to succeed in a game. It's tempting to just go "this game is broken" or "this game is not to my tastes," and that's totally cool. However, there's a huge depth of game there, that includes serious respect for the fictional space in a way few other games replicate, and I think it is worthwhile -- for game design education if nothing else -- to play it aggressively and appropriately and see where it leads you.