Might try getting a copy of FEED ME I'M YOURS by Lansky. This will take you thru kids eating issues at all ages and how to help them.
In addition, you MUST look at your own eating habits. Kids pick up on MORE than you realize. Numerous times, I've encountered kids w/ eating issues and turned around and found that the parents are doing pretty much the same thing.....not trying things, "YUCK" to fruits, vegetables, new foods, picky eaters, etc.
You HAVE to make food FUN AND help them understand why they need good nutrition. Three is the PERFECT age to start! I ALWAYS taught nutrition (EVERY day) to my 3 & 4 year olds, DESPITE some resistance from old habits. Once we made it FUN, talked about WHY our bodies needed certain foods, where they grew (geography) HOW it grew (science), talked about textures, smells, etc. THEY LLLLLLLLLLLLLLLOVED it! Some of those kids are now 13 & 14 and they LOVE the food network, want to be chefs, have NO weight issues, etc. and still practice many of the habits I taught them in preschool.
If you don't know, maybe you need to learn too so that it can be an educational experience and quality time for both of you. Use the grocery store as a learning too, sizes, colors, shapes, numbers, etc. TRY NEW FOOD ALL THE TIME....whether that be weekly, monthly, or whatever. TRUST ME....it's WORTH the time & effort!