I've been a vegetarian for 15 years and have always loved veggies -- so I might not be the best person to ask
But here goes anyways...
One of the easiest things to do is to start with something that you know that you like, and add a new veggie to it (like mashing some carrots with your potatoes, or adding a cup or two of a frozen veg mix to a soup that you like). If you like a certain dip, try it with sliced raw veggies instead of chips.
My favorite way to cook veggies is to roast them -- clean the veggies and slice into pieces about 1/2 inch thick, toss with olive oil, salt, and pepper, and bake in a 425F oven until tender and lightly browned. (I can track down approximate cooking times if you'd like.) It works great with regular potatoes, sweet potatoes, broccoli, cauliflower, Brussels sprouts, asparagus, zucchini, carrots, winter squash...and probably lots more that I haven't tried yet! You can add finely chopped veggies to many pasta sauces, or stir-fry them and serve with rice or noodles.
If you let me know what kinds of foods you do
like, I can get you specific recipes. And learning to like new foods takes experimentation and persistence -- read blogs and cookbooks and be willing to try something a few times even if you don't like it at first. Good luck!