If you're rerolling a new class in the same faction, well, you have two advantages. One, you'll know most, if not all, of the quests having done them the first time. Also, if you're staying on the same server, you'll have access to your higher level character. Take full advantage of its professions and ability to go into an instance and farm up a mess of greens for your new self. If you have a level 70 you're disenchanted with on the same server and in the same faction as you, make use of it when mount time comes: it's painfully easy for a level 60+ to farm up the gold for a level 40 mount.
However, if, like me, you're rerolling on a whole new server to join up with some friends, you won't have those advantages. You may be rolling a new class, in a new faction, on a new server even. If this is the case, don't just forget your experience the first time. There are quite a few quests that are not unique to either faction, especially once you get into the late 20's/early 30's. Zones like Desolace, Strangelthorn Vale and Ashenvale provide many quest opportunities for horde and alliance both, and while many of the quests will be different, the zones themselves aren't: don't throw out the baby with the bathwater, so to speak. If you knew where the Satyrs were when you were an alliance hunter, you still know where they are as a horde warlock. It also bears keeping in mind that the new Burning Crusade starting areas have lots of quests all closely packed together and you can take any character of the same faction to those zones - you could easily level a tauren warrior to 20 in Eversong and the Ghostlands. Take advantage of this new content, it makes leveling to 20 much easier and has better gear rewards than the original zones.
Some people reroll to experience a new character, of course, while others reroll to get away from a bad server or to play with others. It's hard to make generalities in this case, but if you are rerollling to play a new type of character, please consider playing one of the hybrids, as you'll have more options in playstyle than you will otherwise. If you're used to warriors, you can go enhancement with a shaman or ret with a paladin, easing yourself into the new experience with a minimum of effort. LIkewise, if you've played a hunter for a while, a warlock provides both ranged DPS and a variety of pets while still being very different and thus, new and exciting. Of course, you may well desire to get as far away from your original character as possible, being sick of tanking for instance and wanting to try out a mage's robes instead of a druid's leather. In this case, it still helps to keep your old class in mind, mainly to prevent you from trying to do with the new one what you did with the old. A mage can AoE farm but does not want to try and grind with the lack of downtime of a feral druid, and if you try it on your new mage you'll be running back to your body a lot. If you're embracing a new role, don't fall back into old habits.
I personally don't use levelling guides, but a lot of players swear by them, and they make switching factions or classes easier. Jame created one of the first and most famous ones and I'd be remiss if I didn't mention at least that one. I'm sure the comments will have better ones, but like I said, I don't use them and am not familiar with them. Part of the challenge of the game for me is finding my own way there. You'll have to make up your own mind there, though - if you're rerolling because your raiding guild needs a healer, for instance, then you may want to get there as fast as possible. (Then again, if that's the case, your guild should be helping you out.)
That's enough from me, I think. Feel free to share your rerolling advice and give tips as well as just explaining your own experiences with starting over.