I've been doing Ornish's plan for a little while now (it's vegetarian) and it has reminded me of the eight years I was a vegetarian. I thought maybe I'd post some of my hints (from way back and the new ones I've been picking up).
How do you deal with the challenges of dining out? Especially when you are in the company of people who will order a steak the size of their head if it is available
Depends. Are the challenges with the people or the dining out?

People are easy to handle. Most of them don't notice that you're eating vegetarian unless you point it out. (Like throwing down the menu in disgust and yelling, "there's nothing I can eat here!") Once in awhile, I dine with a friend who tries to bait me into an arguement. Usually if I say something along the lines of "I, personally, couldn't kill this so I feel bad eating it. It's just my choice." or, "It's something I'm doing for me." As far as dining out, you'd be suprised how many things are vegetarian or can be adapted that are on the menu.
Any suggestions on making good food choices or favorite places that you go to that offer alternatives?
Soups. I frequently find vegetarian soup on the menu. Check the stock choice though. Make friends with the chef of your favorite resturant. If you're a regular, they'll usually go out of their way to please you. Any hippie joint.
And how do deal with eating on the run and fast food joints?
I thought this would be the hardest, but I find it the easiest. You just got to think out side of the (happy meal) box. Fast food for me has become the 7-11 or mini-food mart. There's always yogurt or cottage cheese that is in a safe sealed container with an expiration date (who knows about those rotating hot dogs!). Burger King's BK Veggie is yummy if I can't get away with no fast food and Wendy's has a great salad. Yes, there's the obligatory "side salad" but GAG ME. Usually, I can find something much more appealing somewhere else.