I want to help nurture but when I do the egg only seems upset by my nurturing. What type of nurture is needed for each species's egg to make them happy?

Hatchlings:

Derpy-Read a book
Weak-Work out with them
Slow-Race with them
Hungry-Offer them food
Restless (or similar)-Play with them

Eggs:

Restless-Turn them
Cool-Warm them
Warm-Cool them
Dull-Polish them

I had the same problem when I was new. At the top of the window that pops up, there will be a little message saying, "This hatchling is [insert adjective here]." You want to make sure to click the corresponding button. Follow the guide posted by the considerate player above me to make sure you get the button right.