There are two different aspects in facebook platform.
first is graph api, http://developers.facebook.com/docs/reference/api/, which is abstract concept and independent of the SDKs. [this used to be the old Rest API, but FB is not moving to graph api]
Second is the SDKs that offer easier way to invoke this graph api. http://developers.facebook.com/docs/sdks/
Then there are social plugins for sites, which I consider icing on the cake http://developers.facebook.com/docs/plugins/ :)
There is not much science behind it. Once, you understand graph api and structure of information, try to get SDK(examples) and retrieve/manipulate some information on a test account. [creation/deletion of test account itself is now done by graph api(or may be old rest) calls.]
For beginning FB development, I have found the FB documentation itself to be enough. However, if you don't know all this background then it is a bit cryptic.