I just got started playing again last week after a nearly 10-year and 2-editions long hiatus. I got a group of my best friends together, none of whom had ever played any tabletop game other than monopoly. I was of course the DM, and using a modified version of Keep on the Shadowfell adventure (with some of my own modifications), and it went great. That map teaches the basics of dungeon crawling very fast (and the importance of checking for traps).
Some advice... hmm, well, I'd say the two main things any DnD'er needs to follow:
1. Be creative! If you're a player or DM, come at the game with an open mind and creativity and you'll help add to the experience. This is no video game or adventure book, you can (try to) do anything you want to. We've all had this experience, probably at least a dozen times per video game, where we thought to ourselves "Well, why can't I try tackling this problem like this?", but of course the game wasn't programmed to allow for that. But, now you can try all those crazy ideas! I mean, no guarantee they'll work but.. offer yourself up to the Dice Gods, and maybe you'll get lucky.
2. Know your group! Several people have said "have fun with the game!", and several others have said "be serious!", well, those are both right, depending on the situation and the group you're in. Try and fit with what the group as a whole wants. Do they just want a silly campaign where limbs are routinely chopped off, flaming vomit is used as projectiles, and genitalia is used to channel Ki strikes (all of these things happened in my last game)? Or do you guys want a serious adventure with a great storytelling? Or some mixture of them? You should all decide what you'd like out of the game as a group.
Hope you guys have as much fun with it as I have
P.S., 4th ed., at least the combat, is awesome. Any other problems with it can be overturned or tweaked by any DM worth his salt. Just like every other edition.
edit:
P.P.S. Playing in 4th, bring back critical misses on a natural 1. And don't let your DM be lazy, be creative in what a critical miss means! Randomness is the spice of life.