Start early. It starts during infancy. You should start by only introducing vegetables to babies first. When babies start on only veggies, it helps keep them from wanting sweets, since all they know is veggies. When you do begin introducing fruit, blend it with vegetables so it's not as sweet.
Reintroduce foods. Research shows that frequent exposure helps shape taste buds. It typically takes about 5 times before children will stop rejecting a food. Also remind older child taste buds change; things they use to not like, they might now.
Try two bites. Children must try two bites before they can say they don't like something.
Make it fun. Involve children in cooking.
Games and activities such as "plant parts we eat", keeps children interested and excited about eating. Another fun activity, is "Baby birds getting feed". Children can pretend they are an animal and their food is what that animal eats.
Healthy food first. Have children focus on their healthy meals first, and then other snacks. Have an understanding of " you only get dessert if you finish dinner". Serve dinner and set a certain amount of bites they have to eat of veggies, before getting their favorite part.
~Bonus Tip~
Blend/mix flavors. Don't be afraid to mix things up and make a rice bowl or other dish with veggies "hidden" in them. For infants, you can make fruit and veggie puree to mix with yogurt. Older children and even adults will enjoy fruit puree and yogurt.
Here are some links to silicon trays to help with your blends.