My kids (8 & 5) love their vegies.
We grow whatever vegies we can, this involves the kids from the start. They help plant the seeds and then water them, talk to them, pick them ,eat them.Sometimes, the vegies dont even reach the kitchen. Quite often they are in their cubbyhouse munching on cherry tomatoes or beans or even chives.
The next thing I do is explain to them why they are good for us, I go through whatever vegie we are having and teach them. eg Spinach, I use the Popeye muscles analogy for my son - loves his spinach cause he wants strong muscles.
My kids usually help me cook dinner,. I make them a vegie platter to munch on while we are cooking, usually with a avocado dip. My kids love cooking so I involve them with it - even if its grating a carrot. By the time we have dinner they have had a couple of servings of vegies. They are more happy to eat their vegies because they have been involved in the process.
Im a good cook and detest the soggy boiled vegetables that I was served as a kid. Any wonder kids dont like vegies. I usually steam, stir fry or serve them raw. Sometimes I make a 'cheese 'sauce (made from pureed cauliflower and herbs etc - my son has food allergies so cant have cheese)
When my son was going through his 'meat only' stage, I made faces out of his dinner. Chopped up lettuce hair, grated carrot beard..
If these starategies dont work, You can just hide the vegies in their meals, "fake it till you make it". Spagetti bolognaise hides so many vegies, so does meatballs and pies. Kids love pies .
I dont give my kids a choice, there is no dessert till they have had their vegies. I wont allow them to eat rubbish, a few treats every now and then. I dont make a big deal out of it though. Eating shoudnt be a stressful thing. You want to create an enjoyable atmosphere.
My kids are the best, my 5 year old said to me this morning - I kid you not "Thanks for not giving us much junk food Mum, i like being healthy" That is a reward in itself.