Short answer: cultural appropriation is "taking intellectual property, traditional knowledge, cultural expressions or artifacts from someone else's culture without permission." 
Basically, if it's not from your culture and you use/do it without permission, it's appropriation.
It's not really as explicit as asking every single member of that culture to sign a permission slip to appropriate from them. If you feel inclined to take something that you know is from another culture, it's important to know its significance and history first, especially if it's something sacred. 
If it comes from a culture that is not yours, then yes you should research first. Google is your friend.
Usually, if not always, cultures that are appropriated by "dominant" groups are those that belong to minorities--groups that are oppressed in society. It exploits them and it doesn't give them credit due to them, instead the glory goes to the "dominant" people who have appropriated them. By appropriating their culture, the "dominant" group tends to enforce stereotypes, usually negative ones, of the people whose culture they appropriated.  Cultural appropriation is also a by-product of racism.
The "dominant" group (i.e. white people) are usually the perpetrators of appropriation.
Not at all. If you take from a culture that isn't yours without permission, it's still appropriation. It just so happens that white people are more prone to this because they are considered the "dominant" culture.
Much like reverse racism, there is no such thing as white culture appropriation. Not because there is no such thing as white culture itself, but because white culture is so dominant in society that to partake in it is not appropriation, but assimilation. Sure, minority groups are able to mock or mimic white people and their culture, but it's of no consequence because it does not harm white people in the way the white people's mockery or mimicry of minority culture does.  It doesn't work both ways like that. Because the white people are in a position of power, which they attained from years of imperialization, their mockery of minorities is dehumanization; on the other hand, the minorities' mockery of them is merely satire.
Because it's not fair to appreciate this one thing from X culture because it's hip or trendy or "aesthetics." You're taking something from a culture of plenty of people. If you just use this one thing to appreciate an entire culture, it's not appreciation at all. To appreciate a culture is to be respectful of the culture as a whole, including the people who belong to it. Learn about them. Recognize their struggles as a marginalized group. Listen to them when they speak out against their oppression. That's how you appreciate a culture.  You still don't get to appropriate the thing you originally wanted to take, but hey, at least you have an appreciation of them, which is what you wanted, right?
Sure, there is.
- When you are invited to participate in X culture by someone of that culture.
- If it's a product of X culture being sold, the producer and seller is of the culture and the profit goes to them, not to big corporations that mass produce items that are "inspired" by X culture.
- If you go to X country and their culture inspired genuine appreciation in you (not to be confused with going to a country and being an expert of their culture in just 3 days, because that is not cool) so much that you want to share it with other people back home in a respectful manner. 
Most of the time, it's quite easy to spot someone who culturally appropriates; for example, a white guy doing blackface and speaking in a "blaccent" is definitely racist. But sometimes, it can be tricky. Some aspects of X culture can be found in Y culture. You may encounter someone whom you think is of Y culture but is actually of X culture.  Before you go calling someone out, ask them about it first, or if they're a famous person, Google it. Above anything else, be respectful before being ignorant.
Easy: don't appropriate. But, if you really want to "pay homage" or "show appreciation" or whatever to X culture, be mindful of the people of that culture first. It wouldn't kill you to use Google, or go to a library to learn more. It wouldn't kill you to talk to a person of that culture to educate you, nor will it kill you to give credit to them if you've taken something specific to their culture. It wouldn't kill you to show support and solidarity for a marginalized culture without being offensive or degrading. 
If you really give a damn about a culture and the people who partake in it, you'll do these things to ensure that you're really respecting and honoring their culture and not just appropriating for the heck of it--or worse, to mock or oppress people who are already oppressed. If you don't actually care, well, why'd you read this article in the first place?
- Isis Evangelista
click on photos for sources
P.S. This article isn't for you to ignore other cultures altogether so you won't appropriate them. We should be recognizing and celebrating our cultural differences, but not in such a way that exploits or degrades other people, especially those whose cultures are already oppressed by years of racism. There are ways to respect and appreciate these differences without being offensive or ignorant.