Zoltan, you can find the complete Apostrophe 1.5 documentation here:
The so-called "designer's guide" is relevant for frontend CSS development (it's a bit misnamed).
I would strongly encourage you not to use A1.5 in new projects, but it's reasonable to keep maintaining it. We do so for several clients.
The designer's guide will help you figure out where your LESS CSS goes. There's also a deployment guide that will give you some insight into how we usually set it up.
As for the mechanics of doing responsive CSS development, that really isn't an Apostrophe question. It's a general CSS question and there are many resources to learn about that online.
Good luck with your project.