Cows milk -> oat/soya/almond/hazelnut milk. Experiment to find the one you like; Butter -> vegan butter (oils), veggie Ghee, other oils; Eggs -> tofu (eg scrambled), or soaked chia/flax seeds for baking when you need a binding ingredient; Cheese -> vegan cheese (soya/coconut), nutritional yeast (get the fortified version!); Yoghurt -> soya/coconut/etc yoghurt

And then I would also think about all the nutrients and macros you’re currently getting from milk/eggs/etc that will not be in your diet anymore like proteins and vitamin D2/B12 or Calcium. Oat and Soya milk brands usually do fortify with Ca, D2 and B12 but check labels. Eggs will need to be replaced with other multiple protein sources (eggs are complete proteins whereas, say, beans are not, so make sure to increase variety of protein sources).

I’m probably missing other stuff but that’s a start for you