Received offer to work for free, how to negotiate for a salary?
The question you have to answer is:


  Can you go for one year without eating and living under a bridge?


As I assume the answer is no, you simply tell her you cannot work without getting paid. She shouldn't be offended by this.

Even if she has no money, she may know other labs that have, and can recommend you My master's advisor came one day with a friend of his and said "this is Prof. Smith, and he is looking for a PhD student in a project I think will interest you".

Lastly, depending on the country, working for free may be illegal. In Spain it is common to do PhDs unfunded, in Sweden it is considered slavery.