Jungling is the only way of playing Udyr! He sucks on lane, because he cannot harras and none of his strenghs will be used.

Tiger Stance:
Activation - Udyr's next attack will deal a high amount of damage over 2 seconds, and Udyr's attack speed is increased for a few seconds. Persistent Effect - Udyr's attack speed is passively increased.
Persistent Effect: Increases attack speed by 20/25/30/35/40%.

Activation: Udyr's attack speed is increased by 15/20/25/30/35% and Udyr's first attack rends his target, dealing an extra 30/80/130/180/230 (+) magic damage over 2 seconds.

Cost
75/65/55/45/35 Mana
Range
600

Turtle Stance:
Activation - Udyr gains a temporary shield that absorbs damage. Persistent Effect - Udyr's attacks cannot crit, but he restores his health and mana equivalent to a percentage of his damage dealt.
Persistent Effect: Udyr's attacks cannot crit, but he restores 12/14/16/18/20% of his damage as health and 9/10.5/12/13.5/15% of his damage as mana.

Activation: Udyr gains a temporary shield that absorbs 60/100/140/180/220 (+0.5) damage.

Cost
75/65/55/45/35 Mana
Range
600

Bear Stance:
Activation - Udyr gains a large movement speed increase for a short duration. Persistent Effect - Udyr's attacks stun his target for 1 second. This effect cannot occur on the same target for several seconds.
Persistent Effect: Udyr mauls his target with such force that they are stunned for 1 second. This effect cannot occur on the same target for 6 seconds.

Activation: Udyr gains 15/18/21/24/27% increased movement speed for 2/2.5/3/3.5/4 seconds.

Cost
75/65/55/45/35 Mana
Range
600

Phoenix Stance:
Activation - Udyr sends out pulsing waves of fire dealing damage to nearby foes for 5 seconds and has increased ability power and damage. Persistent Effect - Every third attack, Udyr engulfs enemies in front of him in flame.
Persistent Effect: Every third attack, Udyr engulfs enemies in front of him in flame, dealing 40/80/120 (+0.25) magic damage.

Activation: Udyr sends out pulsing waves of fire dealing 10/18/26 (+0.25) magic damage each second to nearby enemies for 5 seconds. In addition, Udyr's Ability Power is increased by 16/24/32 and his Attack Damage is increased by half of that amount.

Cost
75/65/55 Mana
Range
600

Passive:
Monkey's Agility - Entering a stance grants Udyr 10% attack speed and 3% dodge for 5 seconds. This effect can stack.

* Mana cost of shifting decreased to 55/50/45/40/35 from 75/65/55/45/35
* Turtle Stance now heals Udyr based upon the actual damage dealt (instead of the raw
damage dealt), but the heal is not reduced if the damage is shielded
* Phoenix stance's activation damage increased to 15/25/35/45/55 from 10/18/26/34/42

Ghost and Smite! no discussion

I also tried out Flash, Cleanse and Exhaust but Ghost is the most usefull!

All other spells are not for you!

Armor Pen or Magic Pen reds
flat health yellows
CDr blues
Attack speed Quintessences

I go with 0/21/9, just look at the trees.

Start with the basic Armor and 5 health pots and get the blue golem by two times phoenix and smite, as well as an health pot. It might be easier if one of your mates pulls the golem but it will work anyway. Take another potion if requeired during the wolves. Hit Phoenix on the red wolf and then turtle twice to finish them of. Same with the wraiths: Rush in with phoenix and finish them of with turtle. Try to keep your life over half and "dance" the red Golem. Rush in with Phoenix and switch to turtle and back to phoenix as often as possible. Smite it and get the 2 little golems. If you have done well, you will have one health potion left. Use it and gank immediatly as long as you have red buff.

Hit ghost and turtle and rush in. Right before you hit, change to bear and stunn your target. Now hit phoenix and in most cases this will be successful. If you are in a 1 vs 1 fight, just try to to change between the stances as much as possible.

If you get a kill / FB you will have enough gold to buy your madreds razor and the simple boots. If you have enough gold also buy 2 wards and another 2 health pots.

Mid Game
Continue jungling, ganking and give your mates the chance to shop, by holding their lane, you need the xp. Always remember that turtle gives you lifesteal and manareg as well as a nice shield.
The Buffs.

Blue Buff is nice but there may be some champs in your team that are more used to it. Give it to them!

Red Buff: It is for you! no discussion! Get it as often as Possible.

Dragon: You can do it easily from level 7 by your own.

Late Game:
After level 11 I start to skill the Tiger Stance, cause it is your second real Damage skill! The switch from Turtle to Bear to Phoenix to Tiger and back to Phoenix as fast as possible gives you plus 30% Attack Speed as well as a good Dodge Chance. You can push towers in seconds and squishy Chars will melt.

I usually build Madreds Razor into Madreds Bloodrazor but wriggles is also fine if you think you need more Lifesteal.
After Boots, Trinity and Bloodrazor i buy what is requeired:

Tanky build: Randuins Omen, Banshees Veil/Force of nature and Guardians Angel

Attack speed build: Wits End, Starks Fevor, Guardians Angel

Lifesteal: Bloodthirster, Hextech Gunblade, Guardians Angel

In most cases i differ my build around these Items so i can get what is requeired.

Alternative Build:

Wriggles, Boots, spirit visage, Frozen Mallet, Warmogs, Atmas Impaler

Other Items that works great on Udyr: Sunfire Cape, Malady, Aegis of the legion, Guinsoons Rageblade, Quicksilver sash, Sword of Divine, Black Cleaver, Thornmail, Youmos Ghostblade.

Playstyle:
Although you are quite tanky, you are not the Initiator! You just can do Damage if you are not focused! CC is your biggest enemy. Try to avoid stunns, slows etc...

Two possible ways to enter a Teamfight:

1) Concentrate on their carry and take him out of the fight. Works well if your team is heavy on CC.

2) If your team has nearly no CC, just hit Bear and run around and try to stunn everything.

Pros: Great CC with Bear
Great Damage Output the whole game, even you play tanky
Extremly fast jungling
Great Pusher with Phoenix/Tiger
Great Ganker Earlygame

Cons: Nearly no range
Can be shut down with heavy CC
often focused