The first time I was on this diet, I tried a bunch of veggies like asparagus & salad greens that I HATED before, like with a passion. The only veggie I enjoyed before that was corn & obviously, I can't really have that right now. :P
But now I'm a crazy salad addict - took awhile to find a dressing I liked though (when I was younger, i was all about Thousand Island, now I can't have anything but Italian!). But all I had to do was try it, with a bunch of different dressings - and ta-dah! I started eating them
One of my old landladies used to marinate vegetables too. She had a bunch of veggies I hated like celery & such, and marinated them in italian dressing overnight - they didn't even taste like veggies anymore, they tasted like my salad! It was awesome! I was shocked that she managed to prepare veggies I actually enjoyed.
I also looooove stir-frying.
The other option of course is to "sneak" tiny bits of veggies into other stuff you eat. Chicken breasts with alfredo sauce & little bits of asparagus or something sprinkled all over it? Not bad. Meat loaf with a few extra veggies like peppers & onions mixed into it? Helps a bit. Not a huge serving obviously, but it can get you used to the flavor & texture in little steps, so you ease up into more obvious veggies in your meals.