This guide will inform on how to get, tame, and live with wolves.
Bones. Lots of bones.
You need lots of bones because the only way to tame the wolf is to feed it with bones. Why lots? The number of bones needed to tame a single wolf is random, and may even be whopping 10! And you might come over a wolf pack, and it will definitely need tons of bones to tame all of them. You can, of course, tame just one or two, but then, you'll waste a great chance to get many wolves quickly.
OK, how do you get bones? Well, if you happen to have a mob looter / mob tower / mob farm or whatever you call it, good for you. A large enough mob looter will offer you literally endless stream of bones. Another way is to turn a skeleton dungeon into an automated looter for high efficiency. Or if you are brave enough, you could just wander outside at night for some fierce skeleton hunting. Just watch out and take lots of food with you, such as cooked porkchops. If you get below four hearts, then head back home, killing skeletons as you go. If you die near your house, don't worry, just go to bed and pick up your items in the morning.
Remember: If you try to feed the dog and accidentaly hit the hit button, the wolf and its pack will go hostile and they won't be tameable anymore.
Ashes to ashes, wolves to dogs
OK, you've got your bones with you. Hopefully a whole stack of 64 or even more. Now what? You just sit around and wait for a wolf to pop up? Nope. You just go wandering in the woods, at daytime. Wolves need light to spawn, any difficulty goes.
A neat way to maximize your chance of having a wolf spawn is to place a torch in middle of darkness at night, wander off (they don't spawn very close to you) and come back after few minutes. Since around the torch should be pretty much the only place where neutral mobs could spawn, they will all spawn there creating a huge bunch of them. You will very likely find tons of cows, pigs, and chickens, and if you are lucky, a wolf! If not, you may direct your anger at the local pigs and try again. Chop pigs for pork chops. No, really, some pork can be useful later on, since you can use it to heal your wolves should you be careless enough to let them get hurt.
So, once you find a wolf, equip your bones and keep right clicking the wolf until it gets a red collar. That's your pet then.
Hint: Wolves spawn more common in Pine Forest biomes rather than any other biome
You got your wolf now!
Now you have a wolf, possibly more than one. What to do now, you don't want to be a bad pet owner, do you? First lesson, interacting with your wolf. Clicking it with your right mouse button (with no food equipped) will have it change between two stances: sitting and standing. Sitting wolves will stay put, but will defend you if you come under attack by hostile mobs. While standing, they will happily follow you. Your wolf got left behind? Fear not, once you are too far from it, it will teleport right next to you. Just keep in mind, they can teleport anywhere, even into pools of lava. That's why it's not a good idea to take wolves into caves with you. Also, look out where you stumble. If you cross narrow bridges, jump over gaping gap or do any risky maneuvers, your wolf might get hurt by falling long distances or coming into contact with hazardous objects. Keep that in mind. Always. It is usually a good idea to leave your wolf sitting inside your house if you plan to go spelunking. If it happens to get hurt, just right click it with food equipped and voila, it will regain health. Its tail will show its health level, the lower the closer you are to a visit from the Grim Reaper. If you happen to spot a zombie or skeleton, hitting the enemy in question will cause your faithful wolf to attack it. This also happens with passive mobs. If you get attacked by anything, a skeleton, a spider, or an archenemy on a server, your active wolves will come to your defense. Just keep in mind that wolves will never attack creepers, for obvious reasons.