Some things that are not necessarily appropriation, depending on how they’re done (but can get into really dangerous territory really quickly):

• Learning from another culture
• Admiring another culture
• Seeing things in another culture that are better than in yours, and trying to figure out how make what you do more like that
• Learning values from another culture that are better than yours, and trying to incorporate what you’ve learned into your culture
• Learning musical or artistic styles from another culture
• Learning how to make food associated with another culture

Pretending that what you’re doing is literally the same thing people in a culture you admire do is always obnoxious appropriation, though. Here are some examples:

• Claiming to be a member of a culture you’ve only read about because of how strongly what you’ve read resonates with you
• Using religious ceremonies lifted from other religions completely out of their context (eg: Christians who are really into seeing Jesus as a Jew often do this with modern Jewish rituals; white environmentalists often do this with Native ceremonies)
• Saying that you must have some distant relatives from the culture you’re interested in, or that you must have been a member of that group in another life, and acting as though this makes you yourself in this life a member of that group 
• Reading a book written by an anthropologist describing their perspective on the childrearing practices of a group they spent a few months with, then claiming that you’re raising your kids just like that culture does