If I have a tenant who is on a month-to-month lease, do I have to give them a notice to quit?

Yes--you give them one month's notice. The definition of a month-to-month tenancy is that either party--either the landlord or the tenant--may terminate the tenancy on one month's notice. There are some conditions which allow termination faster, without providing the notice, such as nonpayment of rent or willful damage to your property However, since it is often not easy to both prove that any damage was deliberate (or at least grossly negligent, which is more than "merely" careless) and was significant or material enough to warrant termination of tenancy (courts tend to not evict people for damaging shades or drawing on a wall, for example), it is probably best to simply provide 30 days notice of termination and proceed on that basis.