I am looking for an easy-to-use tool which can visualize the 'inner working' of a class, written e.g. in PHP. What I would like to see are the different class methods, and how they are related (method A calls method B etc). Is there such a tool to create such a graph?
In a further step, maybe there is a tool which also visualizes the 'inner working' of a class (in a reverse-engineering way) of really how the workflow is, i.e. with all if-else decisions etc, what methods are called in what case? 
If anyone can refer me to such a tool (preferably for PHP and Python) I would appreciate it.
Although a lot of suggestions point towards pycallgraph and phpcallgraph I don't think these will do what you want to do - these are for runtime analysis, whereas what it sounds like you want to do static analysis.
I'm not aware of any tools for this, but, given that you're only interested in the workings of a single class and the relationships within that class, with a little effort you should be able to hack something together in your scripting language of choice which

Parses all function names and variable declarations inside the class and stores them somewhere
Uses the information from step 1 to identify variable usages, variable assignments and function calls, along with the functions in which these occur.
Convert this information into the graph format used by dot and then use dot to generate a directed graph showing dependencies.

Given the effort involved, if the class is not too large I would be tempted just to do it by hand!
Good luck, and if you do find a solution would love to see it.
What tools are available to visualize in-class dependencies (e.g. for PHP)?