https://www.youtube.com/watch?v=TfMELYIGaUg
https://www.youtube.com/watch?v=JiM0ZMUo8PM
Have you seen Trick2g's videos for Udyr?
Basic Summary
To succeed as Udyr, you need to max your Q OR R first (R is better for faster clears), your W second, your E third, and the Q/R that you didn't max gets 3 last.
Build
You only need 1 damage item and the rest tanky with CDR. Lately trick has just been getting 30% CDR in his runes/masteries, but if like me you don't have a ton of CDR runes, you're gonna want to generally follow this build.
The purple smite is the best smite in the game, because it lets you go longer without backing. More mana, more ganks, more survivability, easy solo dragons at level 4. Don't even bother with Stalkers, it's not worth it. Likewise for Cinderhulk. It's the best enchantment in the game for Udyr. Warrior is good if your team ahead, but if you want warrior don't rush it.
Is your team doing really, REALLY well? If yes, do this second and rush Triforce. If your team doesn't have a 5 kill lead with no feeders, you're gonna rush this first. The CDR is invaluable, and Godyr needs to be tanky.
You're going to want your Phage first. If your team isn't doing well but YOU ARE and have enough for Phage, get that then go into Frozen Heart.
After that, suit your tank items to the team you're facing. You only need 10% more CDR to get your 40%, so rushing a Banshee's at that point isn't a bad idea most of the time.
Playstyle
Blue, wolves, Red, scuttle crab. From then, you'll be level 3 and mostly full health, you can invade enemy jg and possibly cheese a first blood. Don't be afraid, Udyr is a boss early game. If he's not there, head through mid and possibly get a kill. Grab the second scuttle crab. If you can gank top, DO IT. If not, go to Gromp clear your whole jg. You'll be pretty low when you're finally at Krugs, so be wary of ganking bot, but it's an easy kill if their laners are low. Back, get purple smite, go solo dragon. All you need to do is use your w, WAIT 3 SECONDS, hit the dragon, make sure W is up every time dragon attacks. Easy. Now you just gank in between farming until mid game.
In mid game, you're a godly tank with a stun. Just stun the squishies, chase down the carries, flame them to pieces. It's fun as fuck. Always clear your jg. You're able to solo tank non-inhib turrets once you have your triforce and frozen heart, so if no one is at a turret feel free to just take it. Stay near your team, stay on top of dragons, focus squishies, it's super fun.
Questions?