The first and most effective step of course is to avoid as much processed food as possible. Go closer to the supply chain where there are less additives and dyes. Natural products like vegetables and fruits brought fresh from the market do not have any artificial dye in them. So is the case with fresh meat and poultry. If you need bakery products, try to bake yourself at home to make bread, muffins and cake so that you know what goes in your food. Use pure extracts for cooking instead of artificially prepared ones.
If you have to processed food, read the labels carefully before you buy anything off the shelf. Look for artificial dye colours which are potentially harmful. These include Blue 1, Blue 2, Green 3, Red 40, Red 3, Yellow 5, and Yellow 6. Look around the aisle for options which use natural food colours. Natural food colours include annatto extract, beta-carotene, beet powder, caramel colour, fruit juice, paprika, saffron, turmeric, and vegetable juice. These colours are not harmful for your health and can be used safely.
Totally replace fruit flavoured items with real fruit and its juice. Avoid processed fruit juices and flavoured milk since they have little of the original fruit and more of the artificial flavours and dyes. Remember as a rule that the more brightly coloured an object is, the more artificial dyes it uses. Steer away from the bright eating stuff that fascinates you and the children.