With Pheonix Stance Udyr:
This is complicated, so follow closely:
Always E to engage with champions, then follow up wiht Q directly into to R, or Q directly into W if you are lower on health, then start alternating between R and W, and E every 6 seconds (when the stun is proc'd). After completing Trinity Force however, you should never ever use Q. After trinity force it's really just a waste in champion fights. Only use it in the jungle.
When jungling you should always engage with R, then go directly into Q and then W and then R and repeat. Q, W, R. Bear stance should never be used when jungling as it is simply a waste of mana. After completing Trinity Force however, R shouldn't be used except for Baron and Dragon. It's just a waste of mana at that point to use it on regular minions.
These strategies are designed to maintain the R passive for as long as possible in champion fights, while gaining the maximum health possible with Turtle Stance.

With Tiger Stance Udyr:
Pheonix stance is ONLY needed with Tiger Stance udyr when he is clearing very very large minion waves. It's best to never use it in the first place.
Always Initiate with a stun on champions only, and then follow up with tiger stance into turtle stance and just alternate. Q, W, Q, W, Q, W. Tiger Stance Udyr is pretty straight-forward.
-Madred's is meant to replace Wit's End late game.