At level 10, you gain several abilities including Bloodrage, Sunder Armor and Taunt. To unlock the last two, you must complete your Defensive Stance quest. The horde can get this quest in the Barrens or Tirisfal Glades, so if you're leveling in the Blood Elf lands you'll be making a trip to Brill, but luckily that's not terribly difficult. If you're leveling in the Draenei zones, they have their own version of the quest so you won't have to leave the zone at all. Either way, the quest can be challenging but is not impossible or even particularly difficult to solo, and is the first of several warrior specific quests you'll get as you level up. The Defensive Stance quest usually leads into another quest for a decent green quality weapon at about that level, which you should complete even if you've been lucky enough to get a equivalent or better weapon, as it's more experience and a chance at some money.
While there's not much call to tank anything while soloing, if you can get groups for quests at this point you can start to practice. If soloing you'll probably not switch out of battle stance, and it is possible to get to level 20 without tanking anything at all. I don't recommend this. Try and get in some tanking as you level and gain new tanking abilities - Shield Bash at 12, Revenge at level 14, Shield Block at 16. Disarm is useful whether or not you're tanking, as it reduces the damage the mob can do to you, as does Demoralizing Shout. Another advantage of trying to get in some tanking practice between 10 and 20 is that it can help you develop your stance switching. 10 -20 is also when you first gain your talent points. By level 20 you will have spent 11 of them, so now is the time to consider what style of warrior you want to level up as.
Many warriors choose to level as arms. I personally always spend my first five talent points in Cruelty. This may or may not work with your desired playstyle, I merely offer that a 5% boost to your critical hit rate at these levels is nothing to sneer at. Either way, while leveling try and make sure that you control the fights you pick as much as you can. Clear around quest objectives, killing everything as safely and quickly as you can, and pull harder mobs away from where there will be respawns if you can arrange it. At this level, warriors simply aren't well-equipped to deal with adds and unless you're very fortunate on your gear, you can often be overwhelmed by a mob that you'd expect to kill easily based solely on its level. A poorly equipped warrior is a very weak warrior.
While leveling up, there are a few instances you can consider running. For Horde, you can start running Ragefire Chasm at level 13, and there are several quests available for it in Orgrimmar. You may have to do some grinding in Durotar to get all the quests available, but that's never a bad thing. Most alliance and a few horde may start running Deadmines at around level 15, which is to my mind one of the best designed and most fun instances in the game and which will see gear upgrades in the next patch. If you run it and get a green drop from a boss, hold onto it for a while, if the patch comes while you're still in possession of it you may get a nice upgrade. Just as both factions can run Deadmines but only the alliance get quests to, both factions can run Wailing Caverns at about level 16 or so, but only horde get quests that take them there. Since it is in the barrens, it's easier for Horde to run it, but the boat at Ratchet makes it possible for either group to get their fairly easily and there are some nice drops here for a warrior, many of which will be getting better in 2.3. Finally there's Shadowfang Keep, very accessible to the horde via the Sepulchre and somewhat less accessible to alliance via Southshore. Many of the drops in this instance, once improved by 2.3, will be worth keeping for a while.
General advice for leveling warriors would include taking a gathering profession. Skinning or mining are often good choices. Mining can help you take a crafting profession and level it for later in the game as well as selling your ores on the AH for gearing money (you probably won't be able to craft anything you'd actually use at this level, it's more aimed at later in the game) and skinning is good because at this level you often kill things that are skinnable, allowing you to auction or even vendor the skins for quick cash. Note that auctioning is almost always more profitable, but vendoring can be much faster if you're trying to level more quickly.
At level 20, you gain the first of your 30 minute cooldown abilities, Retaliation. Once an absolute powerhouse of an ability worthy of having so long a cooldown, it's been nerfed since until it is merely a good ability, but at 20 you won't have any other panic button so it's still welcome. You'll also gain Cleave and Dual Wield if you so choose. I personally find DWing to be frustrating until I can talent and gear to reduce the miss chance and increase the offhand damage, so at level 20 I rarely do unless I'm trying to up a weapon skill by grinding relatively lower level mobs. Finally, at level 20 you gain a quest, either Yorus Barleybrew for alliance or Speak with Ruga for horde, that ultimately leads to the creation of an excellent mail chestplate for a warrior. Both the Fire Hardened Hauberk (seen on the Draenei next to today's post) and the Brutal Hauberk are well-worth getting for the XP as well as the items themselves.
This should leave you in a good position to begin running to 60 once the patch comes out, if that's your intention.
Next week, we may tackle level's 21 - 40 or we may hit Outland for a 58-70 gear guide, or we may do something else. I know, I'm mercurial.