I had to stop dairy about two years ago. and the key to it in the end was just to stop. Don't go looking for substitutes (soya/lactofree/tablets) just don't eat dairy.
Give it a complete swerve and do that by eating and drinking very differently. Dairy generally blunts the flavour of things and is used to pad them out so go in the opposite direction - so swap big mugs milky tea for small strong expressos. In otherwords go for big changes rather than a small shift. Try making those changes across the board too regardless of dairy, swap big water pints of bear for little vicious whiskys. Make an adventure of it, it actually can be quite a culinary adventure. If theres something that just doesn't work for you without milk then cut that out too for a little while, then try it again after a few weeks. I didn't have too much trouble switching to black coffee, but tea without milk was really not doing it for me, so I stopped drinking tea completely for a few weeks then went back to it and black tea was fine.
The tough bit to start with is more the shopping than the eating, you can be such a creature of habit in the aisle that if you cut something out you get the checkout with hardly anything in your basket, so find some good recipies and shop with those in mind for a while so you get a better balance of ingredients in your basket. The recipes don't need to be all that different either, the dairy is only there to pad things out usually, cut it out a things usually taste better.
If you take it in small steps and rely on subsitutes then its difficult to make the changes stick, stuff like soya milk can be tricky to get hold of and when you can't (or when you are eating out or whatever) its easy to laps back to milk. But cut it out and you're palette changes quite quickly, and on the occasions where you do end up eating dairy you wonder why you ever bothered, it just makes things bloated and bland