Calcium is the main nutrient you could miss by eating dairy-free, the mineral is found in many nondairy foods including sardines, fortified juice, tofu, canned salmon, dark greens, broccoli and bread. Drink a glass of fortified orange juice for breakfast, make a sandwich on whole-wheat bread for lunch and make a salad of dark, leafy greens topped with canned salmon for dinner. Protein is another nutrient you might miss, but most people have no trouble getting protein from sources including meat, nuts and beans.
Avoid most store-bought breads, crackers and cereal, but French bread, saltine crackers and bagels are usually safe. Plain oatmeal, cream of wheat, rice and potatoes are all are OK. Try eating hot cereal with a nondairy substitute such as almond or coconut milk. Most plain meat, fish and poultry is safe, but be wary of products with breading as the breading may contain milk. All fresh fruits and vegetables are dairy-free and packed with nutrients. Avoid produce prepared with sauces.
Check the following!
http://www.godairyfree.org/dairy-free-recipes
If you're hungry, any healthy food starts becoming attractive. To avoid dairy though, it's easier to stick with homecooking (as so many processed and convenience and junk foods, have milk products as one of their ingredients). Read the labels carefully for dairy products before using one of those now while on your rotation diet.
For oils/fats, get some extra virgin olive oil. That, plus salt & pepper, should suffice for flavouring in simple cooking / serving.
eg. Cook (steam is my favourite method, try to end up with soft but not soggy) potatoes, carrots, onions, broccoli, brussel sprouts, and beets as an example selection. If you eat meat, you can use that for protein (else, boil dried beans) For breakfast, you could try cooking rolled oats oatmeal porridge as the main ingredient.