Thevenin's equivalent circuit
In general, find the open circuit voltage (Voc) using whatever methods works: node, mesh, superposition or source transformation (the latter not usually applicable with dependent sources).

Then to find the Thevenin resistance, either calculate Voc/Isc, or short the independent voltage sources and open the independent current sources, but leave the dependent sources in circuit and calculate the resistance that way. A trick that can help in that case is to excite the circuit either with a 1A current source at the circuit terminals and use node analysis, or a 1V voltage source at the circuit terminals and use mesh analysis.

There's a good description of this process and some worked examples here: http://www.allaboutcircuits.com/technical-articles/thevenin-theorem-dependent-source-circuits/

And here:
http://people.clarkson.edu/~jsvoboda/Syllabi/ES250/Thev/ThevVCVS_HOsoln.pdf

By the way, where you use "controlled generator", I've used "dependent source". They're interchangeable.

If you're stuck at a particular point in this process, try a more specific question.