If you have a kosher deli or a kosher section in your supermarket that's a good place to get non-dairy marg, chocolate, biscuits, snacks etc. Anything labelled parve or pareve will be completely dairy free. Also most supermarkets will carry various brands of rice milk, soy milk and soy yoghurt. The non-dairy cheeses are harder to get but they are pretty vile anyway so we just tend to avoid them.
My DS is dairy intolerant and has been on a dairy-free diet for most of his 3 1/2 years (aside from the occassional trial with dairy foods).
For breakfast we go for cereal (shreddies & muddles are dairy free), fruit, toast with dairy free marg (Tomor or Pure sunflower spread) & soy yoghurts.
Lunches can be peanut butter sandwiches, lentil or vegetable soup (I usually make my own as I hate tinned soup), scrambled eggs, baked potato with dairy free marg & some veg. Eating out for lunch is harder since he won't eat egg or tuna sandwiches so it's usually fish fingers & chips.
For dinners he eats a lot of pasta (again usually with that good old dairy free marg as he won't eat a tomato sauce and obviously can't have cheese sauce),lots of veg (baby corn & carrots are big faves - try it with a little honey), sesame noodles with soy sauce & honey, fish fingers or homemade fishcakes, home made fish pie made with soy milk, hot dogs, mashed potato with veg, and yes - sometimes even chicken nuggets with chips!!!
For snacks he can have fresh fruit, squeezy fruit (he likes this when his sister has a squeezy yoghurt), soy yoghurt, plain pretzels or crisps (excpet those teddy bear shaped ones - they have milk in them), most brands of bourbon creams (but check first!), many brands of plain wafer biscuits (again - check), bread sticks (he likes the little winnie-the-pooh packs), tortillas warmed in the microwave for 10 seconds, and some brands of cereal bars - the more grown up ones like Frusli are the most likely to be dairy free.
For treats, many supermarkets stock Swedish Glace non-dairy ice cream. For chocolate your best bet really is a kosher deli - you can even get immitation smarties with no milk in them!
Good luck.