You should start with one point in Turtle Stance when you are going to lane Udyr. The shield makes popping in on the enemys turret a joke, also having the bubble can make ganking easier especially around turrets. At level two you should you you're first point in Tiger Stance so you can start farming minions, tiger is great for last hitting and with this build you're going to need all the money you can get. Third you will get you're first point in Bear Stance and its time to either gank mid or push hard in you're own lane.
From level four on you will want to finish off Tiger Stance and Turtle stance, get Tiger at four and Turtle at five and hop back and forth till they are done. After Tiger Stance and Turtle Stance are finished you can just max out Bear Stance and put the last three points in the Bird Stance.
Exhaust both early and late game it is just a personal preference and having Improved Exhaust is even better. With Exhaust I usually run Improved Ghost it works great with this build.
You could easly use other Summoner Spells with this build, Udyr is a good champ that can take advantage of a lot of the Summoner Spells there are. I like to drop Improved Ghost and Shurelya's Reverie from time to time and pick up something like Ignite and a Frozen Mallet.
The choice is up to you to pick what Summoner Spells you are going to use, these are just what I like to use.
Lastly I put a lot of effort in to team work when I play, that is why this build suits me so well and why I have so much fun playing it.
Being able to switch lanes in a flash to help somebody out and get back to you're own lane just as fast is something I do a lot and this build takes advantage of Udyrs movement speed to the fullest.
Early game in the lanning phase Udyr can stun and take hits very well even with this build. So keep that in mind and help you're team mate if they aren't a tank, you mite want to take some hits for them and keep them alive since you can heal up with Turtle Stance.
Late game I like to lock up the other teams Carry's with Bear Stance's Stuns and focus down there high DPS wile popping in and out of Tiger and Turtle Stance. This will put up Udyr's dodge do to his passive and keep up health longer so you can do more damage.