In America you can say, "Not bad. How 'bout you?". Or, if you really want to sound like a native speaker you could also respond with, "It's going. And you?". Other ways to respond among close friends is, "I am hanging in there" if you are having an off day etc, or you can be really short with "Good. You?". In America it's just a courteous exchange. Generally, to be polite you would ask someone the typical "Hi! How are you?" but if you wanted to demonstrate a more genuine care you would add, "How is your day going?". That's really my favorite. It opens up a possibility of a better connection, with most people getting a bigger smile afterwards.

A polite, neutral respnse is 'I am well thank you, how are you'? BTW there is no one way that would be common to all native speakers. Common responses vary between British and American English speakers, and across age groups, and social strata.

I would normally respond to how are you with "good, yourself?" As Jimmy points out it is mainly used as a greeting rather than expecting an actual proper reply, especially when British people say "Alright?" just say say "alright" back, as it's just a colloquial way of saying hello.

Just don't answer it, simply reply with the same question, or say 'nice to meet you'. The greeting is a formality, the asker is using it as a way of saying hello, and really isn't interested in hearing about your backache, or for you to pretend that you are well. If they really want to know how you are, they will ask more carefully, and you should just tell them.

As a general rule, asking someone how they are is a social nicety. If the person is a stranger, they don't really want to hear about your ills. If you start telling a person you just met all about your state of health, they will quickly get bored/embarassed.