I know that many people like to play Udyr as a jungler, but I prefer laning with him. He is probably one of the best chasers in the game. You can effectively chase down someone running from halfway across the map. This is mainly a DPS build, but with some extra goodies.

I went with mostly offensive masteries, with some defense in there too. Udyr is pretty sturdy, and can do a tiny bit of tanking if needed with turtle. Then, in defense, get the dodge chance, and 1 point in ghost for utility. That will be really important later.

The reason I didn't start with Phoenix is because I almost never use it. It's good for farming, that's about it. As Udyr, after u get two levels on Tiger and Bear, you will be ganking like CRAZY. Turtle also gives you a bit of lifesteal and mana gain from hits, so that's good early game. When chasing, you want to do Phoenix (BEFORE they see you, you will spit fire at them while they are stunned with Bear), run with Bear (speed boos + stun), then change to Tiger (Attack speed and damage on initial hit), and switch between Bear and Tiger. This stun/dps/sun/dps combo is VERY effective. If the enemy is a bit far away, use your exhaust, or if needed, ghost. At lvl 18, using boots of mobility (5 extra movement speed), Bear, AND Ghost, I got a movement speed of 607.

It's good to start out with some extra damage and a health pot. Then boots of mobility really let you run FAST, either away or to an enemy. Remember though, you have to be out of combat for the extra speed boost. Then, phage adds an extra slow when you hit them, and zeal for DPS. Lifesteal with Turtle isn't very effective, so I got an Emblem of Valor. Then, build Trinity Force. You have no idea how useful Sheen is with Udyr. Since you constantly switch stances, sheen gets activated A LOT. Madred's just gives extra damage and attack speed. Then build emblem into Stark's, for even MORE attack speed. Banshee's stops you from getting stunned/slowed cuz you can't do much when that happens. And after getting a lot of attack speed, end with Cleaver. Buy B.F. Sword first.

-Early
It is really easy to get first blood with this build. Since you start with a speed boost + stun, Bear your way into a bush (with a teammate) stun, exhaust, start killing. Then, when minions come, try to stay away from the enemy if they're ranged. You can pop in and out of bushes and stun them to harass. After harassing, use Turtle to get some health and mana back. Remember, don't switch around too much early game because you do not have a lot of mana. Then, after you get Phoenix, just stand in the middle of a minion wave and activate it.

-Mid
The keyword here is GANK! You are incredibly fast and have a stun (and slow if you have phage). Make sure your teammate is close by though. Tiger for turrets. Can probably solo dragon now.

-Late
Run around and wreak havoc. You can 1v1 almost anyone. Also, chase down any running people. With a movement speed of 607, they can't do anything about it. Tiger for taking down structures.