Sorry in advance for the novel, but if you're up to read it, don't skim over it. There's a lot of small things that make a big difference.
Also go 
#RUNES
PRECISION
Press The Attack: Triumph-Legend Alacrity-Coup De Grace
RESOLVE (if you don't feel confident)
Demolish-Revitalize
SORCERY (if you do feel confident)
Celerity-Waterwalking
#BUILD
STARTING ITEMS: 
FIRST RECALL: 
(I'm gonna put items you already have to show you what your build looks like overall)
Then take a deep dive into your jungle to be able to buy some stuff.
AFTER A BIT OF FARMING: 
ESSENTIAL ITEMS (in order of purchase): 
(SITUATIONAL:
/
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) 
You get most of the time, but if they have no Magic Damage then don't bother.
Get if they have a lot of crit or no Magic Damage.
Get if they have a lot of %HP damage and no Magic Damage (for example, against a fed 
).
Get if you're ahead but they have champs that can stop your rampage.
Get if you're ahead OR when you're ahead vs Assassins.
Get if you're ahead and nobody can CC you.
Get if you're vs no CC but you're not ahead.
Get if they're not grouping up but have champs with knockbacks ( ,
, etc.)
ALWAYS FINISH TITANIC HYDRA LAST.
VIABLE BOOTS:
vs a lot of Auto Attackers.
vs a lot of Magic Damage/ a lot of CC.
if nobody is stopping you from splitpushing.
if you're ahead and want to mow down their squishies (but only if they can't stop you).
if you're an asshole.
You're almost always gonna go or though.
#PLAYSTYLE
(IMPORTANT:) Make sure to pay attention to your stacks on Q/W. Don't use your Q or W during your clear if your Q or W is at 2 stacks. Also, at the very beginning of the game, level up your Q and use it when you're in the fountain. When you're attacking the blue buff, auto attack the blue buff once and then reactivate your Q so that you get 2 stacks of your Q passive off without wasting any mana.
If you start on the Red Side (top right), your clear order is Blue Buff - Gromp - Wolves - Dragon. Start Q, then W at 2, then at 3 another point in Q. Make sure to stay healthy during your clear. Don't use any smite charges or potions during your clear to save it for the dragon. If you clear all 3 camps and are at half HP or lower, turn on your W and start basic attacking the Rift Scuttler. The only ability you should use during that time is your W to get two procs off of the lifesteal. Then, do the dragon. As stated above, make sure to keep track of your Q and W stacks. When you get to 75% HP, use a potion. When you get to 50% HP, use smite. Once you take the dragon, take the Rift Scuttler if you didn't already, and then go take your Red Buff. Clear normally afterwards. Make sure to gank a lot early game, especially once you have ,since with Press the Attack as well, you do a ton of damage.
If you start on the Blue Side (bottom left), your clear order is Blue Buff-Gromp-Red Buff-Dragon. (the italicized text means its the same as above) Start Q, then W at 2, then at 3 another point in Q. Make sure to stay healthy during your clear. Don't use any smite charges or potions during your clear to save it for the dragon. If you clear all 3 camps and are at half HP or lower, turn on your W and start basic attacking the Rift Scuttler. The only ability you should use during that time is your W to get two procs off of the lifesteal. Then, do the dragon. As stated above, make sure to keep track of your Q and W stacks. When you get to 75% HP, use a potion. When you get to 50% HP, use smite. Once you take the dragon, take the Rift Scuttler if you didn't already, and then go take your Blue Buff. Clear normally afterwards. Make sure to take advantage of Blast Plants to get over the dragon wall.
During Mid-Late game, you're a splitpusher... sometimes. If the enemy team is grouping up, you splitpush. If the enemy team keeps going out on solo missions, you become an assassin, because almost nobody can 1v1 you. Make sure it's a 1v1 though, because Udyr kinda really sucks in fights with multiple people. Once you take out the person, start to splitpush the nearest lane.
I'm not sure if this is exactly the best way to play 
, but it's the one I find the most success with, as well as the most fun.
If you have any questions, just respond to this post.
