As Alan says, if you're interested in eviction (say for non-payment of rent) you might be looking at a "3 Day Notice to Pay or Quit" (or in some areas a 5 Day Notice).
I'm not a lawyer, so this isn't legal advice. However . . .
A 30 day notice often is used when the tenant is on a month-to-month arrangement. Either a longer lease expired and reverted to month-to-month or you and the tenant agreed up-front to a month-to-month arrangement. In either case, either party can give 30 days' notice to the other party regarding termination of the lease.
Having said that, regulations vary by state, by county, and by city. Further, if you're giving notice for a lease violation, make absolutely sure that the lease has been violated. So, if you can't work it out with the tenant, the best advice would be to contact a lawyer in your area (city/county) who specializes in landlord/tenant issues.
Hope that helps.