If the lease converts into a month to month after it expires then you only need to give one month's notice of the new terms as of July 1. Assuming you serve the notice to quit and increase of rent by July 1 that should be good. If they decide not to pay then you have to go throught the process as outlined in the Anti Eviction Act to get them out.
You really can't get more concise than Mr. Schutz' answer. Be advised - your rent increase must be reasonable.
The foregoing is not legal advice, and nothing in the foregoing shall be deemed to create an attorney client relationship. If you feel you need to speak with an attorney regarding your issue, it is recommended that you contact an attorney with expertise in your area of inquiry. The information related above is purely for informational purposes, and should not be acted upon without speaking with qualified counsel familiar with you specific situation and the laws related thereto.