This might be long but I am currently dairy & soya free for the 2nd time so been there for a long time!
Firstly, if your considering dairy free then you might also want to go soya free, the proteins are very similar so a high percentage of those that can't tolerate dairy also can't tolerate soya. Also get yourself calcium supplements, very very very important! And ask for a referral to a dietician. Be warned however, some GP's don't believe that dairy can be passed on via breast milk, it can and it does, I had a gp laugh in my face when I suggested it, I mean properly laugh in my face, he told me food doesn't pass over in breast milk, so I asked if that meant I could now go and get drunk because that wouldn't pass either? To which he stopped laughing and I walked out!
Butter - substitute for either vitalite or my personal fav is pure sunflower
Milk - there are loads! Oat, rice, almond, hazelnut, coconut ..... As a tea drinker I find oat the best, however in coffee the nut ones are nice
Cheese - check out vegan web stores, if your in the uk then I use a online store calls alternative stores, I find the best substitute cheese is violife
Chocolate! - again vegan web stores, be careful though, a lot have soya in place of dairy, I however like moofree, they even do Easter eggs and advent calendars!
Bread - most bagels, wraps, pitta bread and part baked rolls are both dairy & soya free, if a store has a I store bakery then ask to see their book, it will list the allergens in all their I store baked stuff, it means you might just find some nice yummy bread you can have still, also just make your own, really easy
You can still eat most things, it is a case of just making yourself. Bake cakes using vitalite/pure sunflower, they taste no different, I even use it to make pastry for pie or jam tarts etc. make your own custard using custard powder, I make it with hazelnut milk and it tastes just like the inside of a kinder bueno ...... Amazing! Also check own brand stuff in stores, you tend to find that branded goods have dairy & soya where own brand might very well not, don't get sucked into the whole 'free from' stuff, you pay throu the nose for it and often isn't that nice and you can find the same stuff on the shelf in the regular part of the store, example being jam tarts, in the free from section they are something like £2.50 for 6! Check the store own brand, sometimes they are dairy & soya free and you can get 9 for 99p! Basically just check check check labels, you will be so surprised what they dump milk powder in as it is cheap, I even found it in some brands of ketchup, and I think it was chewits had soya in, crazy lol
Eating out is hard though, nandos is good, they have an amazing allergy book, avoid Chinese at all costs if you do go soya free as soy sauce gets put into pretty much everything! My local Indian is fab and he makes my own curry that is dairy & soya free which I have with plain boiled rice (their other rice, if cooked traditionally, will be boiled in milk) don't be afraid to ask
Think that's it for now, sorry it's long, if I think of anything else then I'll pop back