I have a tenant who has given her 30 day notice to vacate. The 30 days has expired but she is now refusing to leave. What recourse do I have (this is California)?

Well, what does your lease say about "holding over"? If your lease does not address it, then you'd need to refer to your state's landlord/tenant property code. (See the sticky ath the top of the forum for a link for each state.)

Typically, you'd give the required notice (3 day, 5 day, whatever is legal there) and if she still doesn't leave file for eviction.

What is she saying? Have you attempted to contact her?

This is one of the biggest things that makes people not wish to rent out... how to get rid of someone who won't leave.
Many jurisdictions have time limits which can be extended for months and months before the sherrif knocks at the door to physically remove said persons.

Of course, some tenants know this... and use it for all its worth. They get 6 months residence out of one months rent, then go on to another rental and do the same thing over and over again.

Give them a notice of eviction. Or get them to start paying rent again and keep them