Have done it and for years. Plus, we don't eat eggs, soy, nuts, and the list goes on.
One of the first things you need to realized is that you'll hve to cook from scratch, or spend a LOT more money than you're accustomed to spending on food. Because, you're right, milk is in EVERYTHING.
But, then, you'll do well to sit down and make a list of things that you CAN have.
For instance, many dried cereals have milk in them. So do some instant cereals. So, you have a couple of choices. First you can buy non-instant hot cereal. I like to make a big pot of it on Sunday (when dh is home and I can spend the half hour on it), and then put it in tupperware or ziplock baggies in single serving sizes, and then am able to toss a bowl of it in the nuker (sorry, I know a lot of you don't use them, but it's a great thing once in a while!) for thirty seconds in the morning. I can't have soy milk, either, so use rice milk on the hot cereal (rice milk, in my humble opinion, tastes rather like library paste, but is actually GOOD when poured over hot cereal). You can use any number of fruits (fresh, dried, whatever), in it or on it. I usually have a chunk of canadian bacon (mmmm, nitrates...) with it to keep my blood sugar level for a while.
Another choice for breakfast is to make your own bread, which can be SIMPLE, or very easy, depending on how much you want to invest. We had a bread maker for five years, and used it just about every day, till we worked it to death. I'm getting another one for christmas. That makes making bread simple...you throw the ingredients in and turn it on. Otherwise, making your own bread is still very easy, and actually can be kind of fun, if you choose a day that you ahve the time to devote to it. Making your own means that you can control exactly what goes into it (or doesn't...), and though there ARE breads without milk in them, they can be a challenge to find. I use bread for sunflowerseed butter toast. Yummy!
You can also make pancakes and freeze them to pull out when you need them and throw them in the toaster. Rice milk and a dash of lemon makes a reasonable facimile of butter milk, believe it or not! We even use egg replacer and end up with TASTY pancakes. If you can have eggs, you can also get a reasonably tasty french toast. Same deal, you can freeze those, too.
What can you eat for snacks? Make a list. Maybe you can't have cheese or yogurt...but can you have meat? Nuts? Seeds? And lots of fruits and veggies!
Lunch, well, no, you can't have cheese, but again, making sure to check the bread, you can still have sandwiches. You can have salads. Can you have eggs? Egg salad. Can you have fish? Tuna salad. Salad Nicoise. Salmon. Nuts, peanut butter and jelly!!, if you can't have nuts, try sunflowerseed butter, it's pretty darned good! Ever had grilled peanut butter? OHMYGOSH, it's about a million times better than grilled cheese!
Dinner? Oh, it's EASY. You cook a lot from scratch. You use pure olive oil for most everything you'd usually fry, rather than butter. Mashed potatoes? Use a dairy free margarine (smart balance has a good one) and some chicken broth, rather than butter and milk when you beat them. You need to think outside of the box sometimes. You need to read a lot of lables and make simple things that you may not have had to make before...but really, it can be done.
Just sit down and make the list of things that you CAN eat...and that's a really great place to start.
Meal planning helps a lot, too. Because you won't be able to just use convenience foods, knowing ahead of time what you'll be making makes life a lot easier.
Oh, and you can bake without milk, too. Really! Go over to the allergy forum and they'll share some recipes...