Everything is not processed in some way. :) It was a long journey to figure out a diet for my youngest, who has a myriad of dietary conditions including Celiac disease, but we got there.
First, if something has ONE ingredient, that's what you call a whole food. An apple, a banana, a head of broccoli, a pork chop, tuna, etc. Those are non-processed foods. You can go one step ahead and buy organic where it makes sense to do so...fruits and vegetables, mostly.
Most of her foods are unprocessed or minimally processed. She mostly eats apples, bananas, prunes, gf cereal, lf yogurt, tuna, tortilla chips, and peanut butter. I know that seems very limited, but she's very picky on top of having a necessarily limited diet.
Minimally processed is often more key, as most children won't live on the above diet. When you look at the ingredient list of a food that isn't a whole food, it shouldn't read like a lab sheet. If you can't pronounce a word and it sounds like a chemical, it probably is.
Dyes are listed just as such (Blue Lake, Yellow # whatever, etc) and should REALLY be avoided if at all possible. Essentially, there are "processed" foods that aren't so bad, but steer clear of long lists of chemicals and dyes. These things have been proven to cause problems in children.
One good example...my two year old LOVES Delimex Tamales (beef) and they are gluten free, so we keep them in stock. Here's the ingredients list, taken right off the box:
Water, corn masa, cooked beef, soybean oil, beef broth, tomato paste, and contains less than 2% of salt, chili peppers, modified cellulose, cilantro, garlic and onion powder, jalapeno peppers, spices.
The only thing that might throw you is "modified cellulose" if you aren't familiar with it, but it is naturally derived from plant tissue, seeds, or wood, and is essentially used to improve texture, retain moisture, and lengthen shelf life (without the use of chemical preservatives! Yay!)
So essentially, even though this is a common frozen food product I buy at WalMart, it is made FROM whole foods and it is NOT full of ingredients I don't recognize. In fact, I know what everything in it is.
Now, for an alternate example...here's the ingredient list on a box of PopTarts (Frosted Pumpkin Pie.) Bear with me!
Enriched flour (wheat flour, niacin, reduced iron, thiamin mononitrate, riboflavin, folic acid) corn syrup, high fructose forn syrup, vegetable oil (soybean and palm oil with TBHQ for freshness), dextrose, sugar, cracker meal, and 2% or less of wheat leavening (baking soda, sodium acid pyrophospate, monocalcium phospate), corn cereal, molasses, yellow corn flour, eggs, gelatin, cinnamon, modified corn starch, nutmeg, cinger, caramel color, sunflower lecithin, tricalcium phospate, vanilla extract, soy lecithin, cloves, vitamin A palmitate, niacinamide, reduced iron, yellow #6, pyridoxine hydrocloride, riboflavin, yellow #5, thiamin hydrochloride, red #40, folic acid, blue #1.
Yuck. NO FOOD you feed your child should have that many ingredients, unless you made an awesome stir fry full of tons of different spices and vegetables. Several of the above ingredients are very obviously chemicals and dyes.
Anyhow, for breakfast...gf waffles with peanut butter, unprocessed cereal, yogurt, bananas, apples, prunes. Lunch is usually tuna, chicken, or tamale with same fruits, yogurt, or a veggie. Dinner is always something different, but common meals include...well, homemade anything, really.
I'm sorry I got so long winded, but hopefully that helps a bit.
Just look for foods that have one or few ingredients, or all things you can recognize.
Also, it's a good idea to shop the perimeter of a grocery store instead of the middle...produce, fresh meats, dairy. Can't go wrong there!
I will agree with Jo to the extent that diet is not a way to treat conditions besides dietary conditions (I'm not in the camp of using diet to treat ADHD)...but if you eat better, you feel better, you behave better, etc, and I think that's just a fact of life. I am all for a natural, minimally processed diet, simply because I think everyone ought to eat that way. I've lived both sides of this, and I can tell you that I have more energy and get almost no migraines eating this way, vs. the sluggishness and constant migraines that came with a really crappy diet.