So you want to be a successful Udyr do you?
This is my BEST form of playing him.
This guide cannot teach you HOW to properly use him, but it can give you a good build and guide on how to use him.
One thing is to know when to use what skill and how to use it.
What some people do not know is when you go into turtle stance it gives you shield (that is known), you can then instantly go into another form like tiger as I do and you retain the shield for a few seconds or until the shield is broken which is what a lot of people seem to not know about.
The shield is really good especially when you use it then go into tiger stance or bear stance, turtle for shield, bear to stun, then tiger to kill. You can spam Tiger to really do massive damage

If you have a nice team then I will start at blue buff, I will hit it first and have a range char hit it a few times instantly casting Q and then Smite (tiger form), then spamming Q until its dead. (only need help IF you get the vampiric scepter first, else if you use the cloth armor and 5 pots first then you have no problem soloing it.
Normally I hit blue buff, then go up to wolves, then switch to golems, ghouls, then red buff.
dragon normally comes at around level 6 if you are playing well and you have the lantern and sheen atleast.

The best thing about udyr is he can be a beast if played proper.
My favorite part about him is once I get my lantern, boots of swiftness and sheen is hiding in a bush nearby, then instantly flash and bear form toward the enemy stunning him fairly quickly and instantly switch to spamming Q 2 times then going back to bear form for the stun and if need be hit turtle (W) and get some health up in the process which usually does very good esp once you get going and learn how to play him.

Most teams like to gank blue buff from the bat, I hide in the bush by blue buff where I can see the buff, if I see anyone coming especially if its more than 1 person or someone I fear from the start then I will just flash over the forest towards the wolves and go past them into the turrets and go over to golems and work my way down.

A Pro on him is that he can be a major tank dpser if played the way I stated.
Pro: Can use minions to easily heal himself in turtle form and if built up even in tiger form.

Con: Gets Ganked in jungle alot
Con: If you are good, you become a big time target because of how powerful you become.

As far as the items go it really depends how you wish to play him.. If people seem to be getting away from you very easily still yet somehow, grab frozen mallet over the black cleaver, if this still isnt enough due to getting hit by magic damage or physical damage and getting raped then choose force of nature or thornmail over the blood thirster.
I usually end up with Force of Nature and Frozen Mallet over thornmail, cleaver, and thirster due to the turtle stance having so much heal on it especially when you already have the lantern with life steal with the infinity edge on top of that being able to heal in tiger stance while doing massive damage. I definately love the mallet due to the fact that it looks like your enemy is in slow motion and even if they flash away, bear stance away and hit them again if your flash happens to not be up..