I know what proxy does and how it can hide the IP address. But how does it really work? I would like to know how it hides the original IP and creates a new one.

For example I have a website, how will I know if the person is using his own IP or using a proxy?

I found this on the metacafe site (I visit daily) and it might help. I have never actually thought about it before, visitors to me are visitors. I guess I have always thought as long as its not a bot I am okay with that.

Hiding ip has become very common. You can find lots of working ips and proxies lists in one search. But "how will I know if the person is using his own IP or using a proxy?" is very important. Imagine a person changing proxies and clicking himself to increase $$ in PPC.....so there are ways to restrict such efforts though I have not gone into details but check this link...... you can make array in php which will contain list of ips used.

it's a good option if you want to escape through a firewall at work or if you're at a place where ceratin sites are censored XD