Udyr players will often start in the jungle and only appear to gank in lanes. Try warding key locations to keep track of his movement.
Once the initial shield effect has faded, Turtle Stance is weak against other champions. Press the attack to force him to switch stances and prevent him from regenerating health.
Some Udyr players buy tank items to become very durable. If they do, focus their weaker teammates instead.
It's essential to plan ahead which abilities you will learn with Udyr. Every ability has multiple usages and five levels. The max champion level is 18, limiting one of Udyr's abilities to rank 3, or two to rank 4. Typically, a player would choose either Tiger Stance or Phoenix Stance as their main source of damage.
Tiger Stance deals high AD burst damage and gives a strong attack speed steroid, giving great dueling and objective destroying ability.
This is usually referred to as 'Stance-dancing'. With the help of Monkey's Agility, Udyr gains flat movement speed and attack speed boosts which stack up to three times and increase his damage per second. Keep an eye on his mana as repeatedly using stances easily drains him of his mana due to the higher mana costs at the early tiers of his skills.
When pushing waves or attacking objectives, alternate between your offensive stances as long as your mana is sufficient. Be careful when using Phoenix Stance though, the AoEmagic damage can hit enemy champions and draw turret aggro.
In late game stages, Udyr can act as a powerful solo objective destroyer by alternating between Tiger Stance (gives attack speed plus the 15% on-hit attack damage) and Turtle Stance (to reduce damage taken). Should the enemy team draw near, Bear Stance'smovement speed boost helps to retreat quickly.
You can engage with Bear Stance to stun an enemy champion before switching stances or targets. But consider that the persistent effect has a 6 seconds cooldown for each individual target.
Using your stun before activating Bear Stance's movement speed again can drastically help by increasing the distance to your enemy when escaping.
Against some champions, it's wiser to refrain from using your Bear Stance stun early until it's really needed (e.g. to interrupt Katarina'sDeath Lotus), since that gives the enemy 6 seconds until they can be stunned again.
Udyr's is a pure melee-focused fighter. Therefore, he is vulnerable to kiting. Try to avoid ranged harassment and crowd control. In early game phases you should coordinate with your allies to encircle targets or wait for them to initiate as Udyr usually needs to all-in at engages.
Udyr lack of ranged gap-closers and his low mana pool can make gank attempts quite challenging if the enemy didn't heavily overextend. As you need to get into melee range first, consider using Turtle Stance before a gank to minimize damage from the enemy.
The classic Flash + Bear Stance combo is the probably fastest way for ganking, as Udyr's primary problem with ganking is reaching the enemy in time.
It's helpful to ask your allied laner if the enemy champion has used Flash, displacements, or disengaging abilities (like ranged CC) recently to make sure you don't waste your summoner spells for a single gank attempt.
Being a pure melee champion with no ranged abilities, Udyr relies on high movement speed and defense to stay mobile and resilient. His build options are very flexible as you can mix-and-match many items with the effects of his stances.
While Udyr is not very item-dependent as others in the early game, mana problems can occur if overusing abilities carelessly. The need of mana and mana regeneration decreases with the game's progress, though.
Sheen gives small spikes of bonus damage along with mana. Consider this first if you don't need Phage's passive speed boost.
Tear of the Goddess is probably the strongest mana sustain for Udyr and it builds into Muramana later. He can charge it quickly by constantly switching around with stances. This also proves useful for a splitpush oriented build where you would need more mana than usual and profits from defensive mana items like Frozen Heart thanks to the high mana pool.
If Udyr can acquire Crest of Insight most of the time, you don't need to build any mana regeneration items at all. This is usually the case if your mid or top laner aren't very mana-dependant or they are building another source of mana sustain.
As most defensive and some offensive items also grant cooldown reduction, consider capping this first if you want to constantly use your abilities.
Udyr is very susceptible to crowd control and heavy slowing effects at first since he has no gap closer with range. Mercury's Treads or Boots of Swiftness have highly helpful attributes to mitigate these weaknesses. The increased movement speed is handy for easier juking of enemy abilities.
Turtle Stance is your primary defensive skill which should be used often as possible if heavily pressured by enemy attacks. It effectively relies on armor and magic resistance to increase its endurance further.
Banshee's Veil packs a few health points more and is effective against targeted CC or burst damage which would otherwise stop you in your tracks.
If in need of an engage-type item, Righteous Glory can provide some beneficial stats and a useful active for Udyr in early/ mid game stages to get in position. In conjunction with a supporter providing speed-boosting effects or abilites, Udyr's ganking or engaging ability can be improved to a formidable degree.
With his good scalings, Udyr can also afford some offensive equipment. However, if you aren't that confident, always consider survivability over offensive items as a wrong build order backfires quickly if the enemy manages to lock you down. Your choice between Tiger Stance and Phoenix Stance can also affect the build path.
Ravenous Hydra gives high attack damage which allows for lethal burst to quickly eliminate high priority targets. The passive gives Tiger Stance pushing power and procs life steal as well, increasing his sustainability in close-up fights immensely, even further if Spirit Visage is in your possession.
Maw of Malmortius is very powerful addition with multiple benefits. Not only does the passive shield increase his survival chances against magic or true damage (as true damage is counted as "spell damage" in some cases), but also increases his strength at critical health. In conjunction with Turtle Stance, Udyr becomes even more a force to be reckoned with.
Blade of the Ruined King grants more sustained damage, especially if the enemy tends to stack health. Its active effect grants Udyr another source of soft CC to improve his chasing, dueling or disengaging potential.
Wit's End and Devourer grant massive attack speed to increase the ratio of Phoenix third hits. The former's passive grants Udyr a source of pseudo-magic penetration which boosts his own magic resistance if he keeps attacking, and when the latter is fully stacked into Sated Devourer it allows Phoenix Stance to proc every second attack, effectively boosting Udyr's DPS.
Against a laning Udyr, it can prove beneficial to make him waste mana by either bait engages and quick disengage or punish him depending on which stance he used. This can easily hamper his early game lane presence, which forces him to regain his lost mana by either using up his potions or recalling to make him lose some experience and farm.
Once he gets some of his core gear, an Udyr alternating Turtle Stance and Bear Stance is one of the harder champions in the game to chase down. Bear Stance's effect can easily make you regret chasing him if back-up arrives. It is best to provide vision before attempting to commit and kill him and being aware of the whereabouts of his teammates.
Disabling Udyr from attacking or switching stances can reduce his threatening power, for example Renekton has a potentially longer stun duration.
Also, whoever can exceed Udyr's own speed (champions like Hecarim, Rammus) will be able outperform him and escape better.
Singed is an effective counter because Udyr has a hard time reaching him without gapclosers, even with slow reduction. Just focus on movement speed and health/armor items.
Be aware of his primary stances and item build:
If he maxes Tiger Stance, he will take mostly AD items and some attack speed. Counter it by boosting armor and health and know that his Q hits will do surprising damage over time, so you might lose a bunch of HP in the few next seconds.