To get milk, you need to get some Frisian Cows in your pasture and they will give you milk. Then you can either eat the milk, or take it to the Dairy to convert to Cheese/Butter/Cream.

There is also an Animal Pen, which requires 4 domesticated animals to build, that produces milk. Now that there is a stable (produces domesticated animals), it can be easier to build a pen than wait for cows to show up with a trader. From what I've seen, two of these milk pens will supply a dairy (with 2 workers) with enough milk to work continually.

´There is also a little bug in mega mod; the diary doesn't show up in the UI, so I couldn't build it.
Solution: load the diary mod from isak25 = ketchup, enable it, even it's shown incompatible, it worked for me, now I can produce cheese, yoghurt and cream.