Start off with Wolves then move to the Blue buff. I recommend a leash. After Blue buff you can either A.) Clear jungle normally...wraiths, red, golem. B.) WITH SMITELESS blue buff go to the counterjungle red buff and either steal(going against slow jungles) or ambush red buff bush, either way you smite their red buff to keep them from taking xp.

With this new update Udyr got a huge Chasing buff so we want to take advantage of that.
If you farm properly you should have a static shiv ruffly around 10 minutes. By then you will have at least level 3 Tiger stance which will give you around 280 damage over 2 seconds and 220 damage on hit. That is ruffly 500 damage over 2 seconds from 1 HIT at 10 minutes in game!!! AND if you have blue buff that is 500 damage every 3 seconds. Bear stance at all levels stuns for 1 second. If you stun them for 1 second that means by the time they start running you will be able to use tiger stance yet again. So that's easily over 1k damage in under 5 seconds on top off your auto attacks. Keep in mind static shiv CAN CRIT!!! with his high attack speed and the 20 percent chance of crit from static shiv, it is very likely you will get a static crit.

PROS
Fast Jungler
Fastest attack speed in game with tiger stance
Great chaser
Fast Movement
Anti-carry
Great burst damage
Short cool downs

CONS
NO RANGE
Highly Mana dependent
No Ultimate
No reliable escape
Gets focused in team fights
easily kited until bear stance is high level