I have served my tenant who hasn't paid me rent for three months now a 3-Day to Pay Rent or Quit Notice two days ago. Now he begs to stay for another month as he doesn't have a place to go. Now what do I do? He hasn't mentioned anything about at least paying me a portion. What action can I do now? I live in the State of California.

Sounds like a situation where you could approach the individual- and let them know you are going to have to seek "Legal advice" from your attorney... even though you may not, have a personal attorney. Basically, it's a scare tactic used by many. This may create some innovation to move on, or to give you SOMETHING to start with. IF you have to, you'd most likely have to seek professional legal advice.
Call your local courthouse and see where they might direct you.
Good luck!

If the tenant hasn't moved out or paid in full by the 3rd day then your choices are to either let him stay until he pays you (I don't recommend this), or to file a lawsuit for eviction.