In my experience, most people only ever say "how you doing" as a joke, if they're trying to sound funny or creepy. It depends on the area, though. In some places and cultures in the US, it's be common to hear people ask, "Hey, how ya doin'?" Unless you're from one of these areas or part of one of these cultures, it will sound weird for you to use this construction. (It would sound weird if I said it, because I don't have the right accent to say it in a natural way. It would sound like I was acting.) "How are you?" and "How are you doing?" are both fine. In informal situations, a lot of people will also say "How's it going?"

Hi Ricardo, The most common native expression for a greeting is “How are you?” “How you doing?” is slangy and pretty informal. In some contexts that is appropriate! The full expression “How are you doing?” is mostly used for extra concern; maybe your friend was sick recently, so you ask this to see how she is recovering, or maybe she is going through something difficult in her personal life (a divorce, a child’s problems, caring for a parent, that sort of thing), and you want to see how she is coping. Hope that helps!

How you doing? is considered a slang version of how are you doing?

https://www.youtube.com/watch?v=5cIqRzum528. I'm old enough to remember "how you doin'?" becoming popular and mainstreamed after this commercial began airing. The phrase used to be associated (in the American imagination) with seedy Italian mafia-types. Now it's a natural way to ask "how are you?" or say "hello."

“How you doing? “ definitely isn’t correct, and yes, you just said the correct form “How are you doing? “, however, if you wanna say it in a more conversational or casual way, then it can be “How you’re doing? “ . I hope it helps, :)