Try incorporating them in small pieces right into your foods that you're already eating. Shred zucchini/squash/cabbage/mushrooms, etc. into burgers, meatloaf, meatballs, etc. Puree them and add them to soups/sauces - anything that could be thickened. Chop them into small pieces and add them to chili, omelettes, pizzas, quesadillas/tacos/burritos, etc.
I just make sure that at least 50% of my meals are comprised of non-starchy vegetables.