Serious Eats - seriouseats.com

A lot of good suggestions here. But I just wanted to acknowledge that even if you do everything "right" and feed your child perfect yummy homemade organic veggies from day one, they still might freak out at age 2-3 and start refusing to eat veggies. It happens.

To echo the above comments, I think that there is value to continue serving veggies at every meal, no matter what. I always put some serving of vegetables on my daughter's plate, even when I'm 95% sure she won't eat them. I try to vary the kind of vegetable. And at least once a day she eats some of something. I don't make a big deal of it at all, or force her to eat them, or even comment if she doesn't. It's up to her; I just serve it.

I find it can be sanity-making to keep frozen vegetables on hand. We currently have peas, beans, edamame, various Trader Joe's medleys. I heat up a small serving for her each meal. I also give her fresh veggies (carrots cut up small, fresh broccoli, fresh tomatoes) with some regularity, and I'll bake sweet potato for her from time to time.

I also regularly ask her if she wants a taste of what I'm eating. (Assuming, of course, that it is appropriate for her.) I try to encourage her to try new things, but I never want to get into a power struggle with her about it.

Finally, it's good to keep relaxed about your kid's eating habits. Toddlers and their refusal to eat can make you crazy. But after 18 months or so, they don't need as much food as you think they do. My pediatrician told me that a toddler can survive on one meal every other day! So if your kid's eating a few bites of peas here, a couple pieces of carrot there, a slice of apple there, they are getting more nutrition and sustenance than you think. Hang in there and don't trip!