As the mother of several children, I can tell you that children will not starve themselves. Most childhood experts will tell you about the division of responsibility. It's the parents' job to provide a healthy variety of food and present it to the child. It's the child's responsibility to actually eat it. You can't actually force a child to eat... you can threaten, cajole and play games but in the end it's up to the child what he/she puts in his/her mouth and eats (some kids will choose punishment over eating if they really don't want it).
It's nice to provide at least one dish at each meal that you know your child will like. Do NOT offer milk at meals, that's a big mistake people make. Our kids get water at meals but if they're chugging the water instead of eating we take the water away until after they are done eating.
Have set snack/mealtimes. Make the snacks healthy, like a mini-meal. Space out the snacks so he's not eating within 1-2 hours of a meal. Also remember the serving sizes for young children - it's 1-2 tablespoons for a 3 year old. So if he eats 5 green beans that's more than a serving of veggies. Write down every bite he takes for 1 week. Chances are, he's getting more than enough to eat from all the food groups but he's spacing it out over a few days/week than a 1 day period. Most experts agree that many kids do this and it's perfectly healthy.
Many toddlers/preschoolers have 1 good meal a day and then just pick at the other 2. Sit down at mealtime, put the plate in front of the child and engage everyone in conversation. Don't mention the food. If mealtime ends and he hasn't eaten, take the plate away -- he won't eat until the next scheduled snack or meal. He might be hungry but he won't starve and if you are consistent he'll learn to try everything and eat.
When my son was 3 he went through a picky-eating phase. I swear he didn't eat a single bite of food for 2 days and then just nibbled for a few days... but a week later he was inhaling everything he could find as he hit a growth spurt.
The first few days are the hardest but gets much easier within 1-2 days. Good luck.