Have you ever been crushed by an unkillable, super fast bear/phoenix man? Is that why you are here? Or are you here because you want to be the unkillable, super fast bear/phoenix man? Whatever is your answer, this is the right place!! Welcome to my first guide:
Penetrating Udyr's Jungle!

Pros: Fast jungle clear time. Great sustain. Tanky. Good damage. Godlike movement speed. Great pusher. Great tower diver with Turtle. Destroys towers quickly with Tiger. Soles Dragon Lv5 or sooner. Soles baron mid game. Great duelist (1x1). Great at stealing buffs. Not blue dependent mid/late game. Dominates yours and the enemy's jungle. Makes it hard for the enemy jungler to farm. Counters almost all junglers. Easy to understand, simple mechanics. Can stun the whole enemy team every 6 seconds. Good initiator. Good with any team comp.

Cons: No ultimate. Easy to kite. Very easy to kite. Counters minions & towers. Requires you to understand the game. Skill cap related to map awareness. Very different form any other champion. Easy to understand, predictable. Bad initiator. Bad against some team comps.

Udyr has one passive and 4 skills:

Passive:


Skills:


Udyr's skills have 5 points each, so one of them will be missing 2 points in the late game. Because of this, people argue about what skill should be left out. Don't listen to them, listen to the facts.

Your skills effects:

gives you a 2 second DOT(damage over time) physical damage on your next auto attack and a 5 seconds attack speed buff.
This skill is used to nuke single targets, towers, inhibitors, Dragon and Baron Nashor. It synergises greatly with Phoenix and Wriggle's Lantern and scales better than Phoenix.

gives you a temporary shield and life steal.
This is your sustain, with this, jungle camps will heal you mid&late game and the shield will absorb great part of the camp's damage. It's also great to tank tower attacks.

gives you a short burst of speed and a 1 second stun triggered by your auto attacks, that can only stun again that target after 6 seconds.

gives you aoe damage for 5 seconds around you and an aoe burst in front of you every third auto attack or right after casting.
This is your best skill against minion camps, it objectively clears faster than tiger early game.

Skill order, explanation and reasoning:

Wingborne Storm Is the one I would recommend to start with, because it will help you clear faster than any other skill. At Lv2 if there's a clear opportunity to gank a lane pick one point in Blazing Stampede and go gank it, if there is none or if it's the lane on the other side of the map, get Iron Mantle. At Lv3 get one point in Blazing Stampede to be ready for a gank, chase or running away.
At Lvs4-5 pick two more points in Wingborne Storm. At Lvs6-7-8-9 put 4 points in Blazing Stampede to increase your chances of succeeding in a gank and raising general utility. Udyr's skills lower their mana cost with every level, being able to spam bear will make you much faster, increasing your pressure in lanes and farm potential in jungle.
At Lvs 10-11-12-13-14 you should invest fully Wilding Claw. Tiger is great to destroy towers and other objectives, it will also synergise amazingly with your Wriggle's Lantern and Phoenix, skyrocketing your damage and sustain 1x1.
In your last Lvs you can either max Wingborne Storm or Iron Mantle. Iron Mantle will give you better sustain and a great shield to resist poke, one of your weaknesses, while Wingborne Storm will only increase your damage a bit, so I recommend Turtle.

An alternative to this order is maxing Wingborne Storm before Blazing Stampede, but it will decrease your utility for a few Lvs.

The 6 CDR glyphs will let you stack your passive using only one skill so they are essential.

The 3 MS quints will make you faster. Being fast is what makes Udyr awesome it will help you push lanes, reach the carries, clear camps etc.

The 9 attack speed marks synergise with your Wriggle's Lantern and your Wingborne Storm

Counter-Jungling:

If there is one thing that Udyr loves to do, it's farming the jungle, yours and the opponent's. A good Udyr will set the enemy's jugler back by farming the camps on the enemy side and leaving only one small minion, this way the enemy jungler will have no experience, no farm and no buff to keep or give to their laners and will be an easy prey to you if you find him or counter-gank him.

Counter-Jungling Secrets:

A good way to counter jungle is to invade the enemy jungle and kill the enemy jungler as he does his second buff, this way you will get both his buffs and a kill, setting him back, this works great against more inexperienced junglers and junglers that have a weak start.
In this scenario you would get Blazing Stampede Lv2. Use Wingborne Storm before reaching the buff so the first attack trigger the effect, then use it again to trigger it again, if they are still alive and try to run, use bear for the stun, then move in front of them so that you have enough time to use Wingborne Storm again.

Counter-Ganking:

Counter-ganking is the art of foreseeing where tha enemy jungler will gank and defending it. This way you can either stop a gank, kill the jungler and/or laner, remedy the damage done defending the turret or feed. Avoid doing the latter.

Counter-Ganking Secrets:

To find where the jungler might gank, just put yourself in his position. One thing that will help you is finding out where he started, looking for yourself is risky and warding is expensive, so the best way is to look where their mid laner comes from after he leaches(helps with 1st buff). From that buff, the jungler will either invade and try to steal yours, or go to his buff, you have to guess what he will do, he usually gank mid, or the lane they are closer to if it's pushed.

Farming:

Most Udyrs are expected start on the blue buff, but if you buy a mana potion you can go red first. If the enemy jungler tries to invade and get your red before you, he will find an empty camp and waste his time.

Taxing lanes:

Do not tax lanes. If the lane is empty push it to the enemy's tower so their laner loses xp. If either laner is coming back, just freeze the lane

Freezing lanes:

To freeze a lane, just kill enough minions so that neither side pushes alone.

Pushing:

When lane phase is over, push the enemy lanes to their towers to get the xp and gold for yourself denying it for the enemy team by letting your minions die at their tower. If it's safe to, hit their tower.

Don't get caught:

If you are pushing or deep into enemy territory, keep one eye on the minimap, don't be there when the enemy shows up. Warding helps tremendously.

This item is insane on Udyr. Udyr is strong in all stages of the game as long as he is on the offensive. This item is what makes Udyr great in the late-game, Wriggle's Lantern gives tou 30% extra gold from jungle minions and will evolve into feral flare giving 1 magic damage and 1 health per stack, and one stack per big monster kill or champion kill/assist. In the late game farming the jungle like Udyr does, you will be a monster.


If the enemy team has a lot of slows but few stuns & snares, get this one.


If the enemy team has too much CC, get this one.


If the enemy team is very auto attack reliant or their adc is carrying, get this one.

Utility Items:

Buy Those to be more useful to your team, especially if you are behing. The sightsnones help by keeping your team safe from being caught alone in a bad place, the Tiamat and Ravenous Hydra can help with farm and pushing, the Locket of the Iron Solari will help your team on team-fights against an AP heavy team.

Pusher Items:

These items help you clear waves and push faster, items that give movement speed also help you survive any possible encounter.

Diver Items:

Diving is in most cases suicide, Guardian Angel will give you a chance to do so and come back alive. It's not uncommon to the enemy team see your GA and ignore you, in that case, stun everyone with Blazing Stampede and focus their carries with Wilding Claw followed by Wingborne Storm

Assasin Items:

Because Udyr is very fast, he is great for picking enemies off position, these items will help you burst & kill those enemies.

(1v1) Items:

These will give you the power to face any tank/bruiser 1v1.

Movement Speed Items:

Just be the annoying Udyr that runs to their face, stuns and gets away with it!!

Health Items:

"Not necessary for living" ~ Kharthus.

Armor Items:

When the enemy is giving you a lot of phisical damage.

Magic Resist Items:

When the enemy is giving you a lot of magic damage.

CC Resist Items:

For a CC heavy team.

CDR Items:

"I love me some CDR" ~ Udyr

Attack Speed Items:

Triggers your wriggle's lanters's damage and heal more often. Helps destroying towers.

Damage Items:

"It hurts" ~ Random carry.

This is my very first guide, it's not finished, please leave questions, I will use them to improve the guide.
If you want to know how he works with or against an specific champion or if a build or X item would work, just ask.