Then you ask them to log you in by sending a request to an implementation-dependent webpage, with implementation-dependent parameters (which ones are required are--you guessed it--implementation-dependent), telling them to redirect you to your page when you're done. Well, actually, that assumes you're building a website. If you're a desktop application, you'll do something else. If you're on an embedded system that can't open up a webpage, there's another option. And there's yet more flows. Which ones are supported by the provider? You guessed it, it's all implementation-dependent. Oh, and maybe you need to refresh tokens to login the future. When? If? You guessed it, implementation-dependent!
It makes writing a generic OAuth client library hard because there's basically no commonality there. Really, it makes me long for Kerberos as a much saner SSO system than OAuth.