First off, and it has to be said over and over and over again: you are not invincible. In fact, you know all that armor you have on? It just means that you don't have any escape abilities when stuff goes bad. We've all seen the Overconfident Tank in action. Don't be that guy. When you're just starting out, pick your fights. Pull mobs into areas that you've cleared, make sure you keep your cooking and first aid maxed so you can eat buff food and bandage when you're done killing. Properly used, first aid and cooking are a warrior's best friends while acquiring XP. It may not seem like a big deal, but more stamina is always a good thing for a warrior, especially when you first get started and you don't have good gear.
Gear is very important to a warrior. A mage without any gear would have a low mana pool and, at higher levels, would be missing out on spell damage, spell crit, and so on. A warrior without any gear is useless. A level 20 warrior with a grey or bad green sword is half as effective as that same warrior with a decent blue. The effect multiplies as you get more gear for each slot in your inventory, so get the best gear you can as soon as you can, keep it updated, keep it in good repair when you visit a blacksmith or other store. Also keep your training current, as it goes hand in hand with your gear. The gear allows you to make effective attacks and boosts your various stats, the training gives your more options. One of the strengths of the warrior class is a variety of options; our three stances give us possibilities in both tanking and grinding, and in addition to gear and training, you need to keep your understanding of the stances and when/how to switch them current as well.
We've all known the warrior who doesn't stance dance. By level 30, you should have all three of your stances after completing The Affray quest. As soon as you get Berserker, start experimenting with the three stances. You'll of course want to tank most of the time in Defensive but it's best to get used to switching to zerk for a fast fearbreak using Berserker Rage as soon as possible. If you're Alliance, well, you won't always have a dwarf priest (or draenei) in your pocket, and if you're horde, they haven't introduced fear ward on that side yet. There are other reasons to dance the stances... grinding in zerk, you may want to switch to Battle or Defensive to thunderclap the mob you are fighting, or to use one of your thirty minute cooldown abilities.
Also, warriors are unique in that we have three linked abilities that share a thirty minute cooldown. Retaliation, Shield Wall, and Recklessness are the warrior equivalent to other classes' escape abilities, but they're not really useful for escape in most circumstances (although used properly, Shield Wall can be, if you get lucky.) Since these abilities are on a long shared timer, a lot of new warriors will be leery to use them, since they won't have any of them for over half an hour if they use one. Break this habit. These three abilities can spell the difference between life and death for a leveling warrior, so learn to use them judiciously, but use them.
Retaliation in particular is a very good ability for when you're jumped by multiple mobs in PvE. It's best to macro ret so that you equip a big, slow 2h weapon when you use it if you can, and don't forget to position yourself so that all the mobs attacking you are in front of you. Used in concert with sweeping strikes and/or cleave, retaliation can bring two or three attackers down at once. The author of the wowwiki article is correct in that retaliation is more or less useless in PvP now, but I disagree with his dismissal of the ability for PvE. It's a panic button, but as a panic button it can save your hide.
Shield Wall is just going to be delaying the inevitable as a panic button, but if you have a healer in your party it can buy useful time (it's an awesome tanking ability, as it cuts down all damage you take by 75%, giving time for one or two big heals to land) and it can also serve if you're just trying to run to the safety of a settlement from multiple mobs. It's not the highest priority for grinding, but you should have a shield in your inventory so you can make use of it. Well, you should have a shield in your inventory anyway, right?
As a panic button recklessness is the worst talent of the three. PvPing, you'll use it as often as it is up, because you'll always need to do as much damage as possible to that mage before he blinks, freezes you in place, or turns you into an adorable turtle before spending six seconds preparing to set you on fire, but for grinding and soloing it's not really suitable to save your hash... the increased damage you'll take from using it will kill you pretty fast if you're using it when you're afraid you're going to die anyway. It can, however, turn a difficult to solo mob into a dead mob pretty darn quick if you use it properly. Step one, build a full rage bar. Step two, pop recklessness and use your highest damage instants. Step three, profit! Well, when it dies, anyway.
Before I go into a few good pieces of gear for the various levels, I want to say again: warriors have a fairly unique grinding/soloing style. You're not going to be able to kill six or seven mobs at once the way a mage can, you're not going to be fear and dot killing mobs six levels above you or big elites. You don't have a hunter's pet to tank for you, as you're the tank (and man, don't you wish you had someome casting mend pet on you?) and you don't have the rogue's ability to sneak into a crowded place to take out that one quest mob and escape. You're a clanking (well, jingling at the lower levels) target, you don't hide. What the warrior excels at is doing significant sustained damage to one or two mobs at a time and moving on with minimal downtime. You have no self heals outside of potions, so exercise a little caution and common sense (don't try and take on three mobs at or above your level if you don't want to have to bandage and/or eat afterwards, and if you try and take on mobs more than three levels above you, you're probably going to die since you'll miss or glance most of your attacks) you'll find the warrior an exceptional choice for questing.
I made a Wowhead filter of the blue mail drops available for a warrior in the high teens to level 30 or so, and it's a good place to start looking. The important thing is to know when an item is good for you, and when it's not: just because you can equip a mail chest doesn't mean you should roll on it if it's clearly designed for a paladin, for instance. Luckily, most of the blues at this level are strength and stamina heavy, so you shouldn't feel bad rolling on them.
This should hit most of the basics: as always, any further advice for starting warriors from those of us with more experience is always welcome in the comments, as there's only so much room here and always more detail to go into.