Way late, to be buried, but I am an Udyr main and have played him for a VERY long time. I am in the process of writing an Udyr guide, but obviously, because he is one of the most versatile champions in the game, it is hard, so bear (heh) with me.
Udyr has 2 main abilities paths to take, with each one having many variations. Here is the main ones:
Tiger
This is a melee mode stance. It does tons of damage and has tones of attack speed, especially with the AB (Activation Bonus).
The major builds for this are:
The catch is you never want to build only into one category with Udyr. As you see, Randuins is shown in each category. You mix and match, build for what the situation calls for. The same goes for leveling.
Phoenix Stance
This is an AP and small AOE stance. You want to follow the same above advice, but with these categories:
Short answer: If you can afford it.
Longer answer: Early game, mana is scarce and costs are higher. Don't ever be OOM, as you will be dead in the water. Ability cycling is what makes this champ strong, and if you cant E/W cycle to get away, you are dead.
Udyr is special in that with a few base items, he is still really strong. But farm, then take easy kills. Its more about knowing what to level than knowning what to buy. Get a feel for the champ and what you can and can't do before you start doing ranked. Then play safe within your limits when you are behind. Udyr only needs one or two kills to snowball if in the right hands. Start training your hands to be the right hands.
Sorry for the long read, hope this helped. I am publishing a guide for Udyr at some point in the near future, and will send you a message when it is if you still need help. Thanks for reading!