At the store, kids can help pick foods the family will eat together. Ask them to pick one or two fruits or vegetables. They will learn that their food choices are important. They may also be more interested in eating new foods that they chose themselves. As the parent, you still control what kinds of foods will be brought into the house. It may be cheaper to buy canned, frozen, bulk, or in-season produce.
Another option is growing a small vegetable garden. Research shows that when children help grow fruits and vegetables, they are more likely to eat them and also try different kinds. Check with your local cooperative extension service for more information on gardening.