Choosing nearest Server across the globe?

i want 3 dedicated servers: in USA, Europe and China. They all run exactly same website. I want to setup them so, that particular user will automatically talk to the nearest in network sense instance of my web site.

Which options do i have to make this work (I heard, Anycast is for that, what else )? I need both a list of options and simple how-to or link, explaining the setup process.

thank you

Solution 1:

Chris' answer is about DNS, so this one is about anycast :

What is "anycast" and how is it helpful?

I find that anycast is more fault friendly that dns.

A bgp routing change will propagate more quickly than DNS entry.

So if a server become unreachable, removing the route to it will ensure that all traffic goes to one server.

Solution 2:

There's a very similar question here that'll probably be useful to you:

Geo-DNS providers?