There are some very good tutorials for doing some basic or a bit more advanced things in php gtk cairo. However it is logical that they do not cover everything.
But luckily one can go further in using cairo by him self, I provide a single and very simple example script that allows you to discover all by your self things like:
What is the connection between cairo parts, for example between cairo context and source, you discover that you can get the source through the cairo context. Then you discover what methods are there avaialble, how to follow a logical path down to the piece of information you need to get your job done!
This example shows you how to get the current rgb color without having a previous knowledge about what methods or cairo classes to use. Of course some error trial and searching might be required some times in following an aproach of this kind, but I think it is worth cause cairo is an excellent library to work with.