The first stage is to develop a taste for things that can be eaten with no preparation. Bananas, apples, carrots, unsalted peanuts and almonds, grapes, mini tomatoes.
The next stage is to buy pre-cut bags of mixed food. Develop a taste for various mixed vegetables that can be added on top of those microwave dinners. Try and use up some of the stomach room that would be taken up with dessert, otherwise.
After a while ... you get to the stage of preparing your own soups, salads, and cole slaws. Almost anything you need can be bought pre-cut and frozen.
But if you want to include some fresh stuff, begin by preparing small items that can be sliced and easily mixed into meals. Look for tube-shaped squash, sweet potatoes, zuccini. Okra, celery, and asparagus and other long vegetables can also be cut - with the remainder easily wrapped and saved for later.
Sometimes you can't quite keep up, but you'll learn after a while that vegetables don't need to be "pretty" to work in soups.
Vegetables are cheap anyway, if you end up throwing some out because they aged on you before you could finish.
I consider it part of the challenge to eat them before this happens. It's a good feeling to realize you need to go to the store b/c you've eaten all the "good food" in the house - and end up standing in line with an armful of veggies while other people have chips, candy and soda in their carts!