Stackoverflow lets you login with many of your existing logins.
Is there an easy way to do this, or does this involve reading the docs for each of these services and integrating ones own website with the way they operate. They may well be very similar and therefore not much trouble to do, but if there is something that wraps all of these into one, then that will be very helpful.
All of the login providers that Stack Overflow supports use OpenID – see http://openid.net/
In theory at least, that means you only need to write one set of code to support all of them.
(In practice, there are some nice-to-have features, like turning a username into am OpenID URL, that will require different code per site, but that sort of thing isn’t necessary.)