Although the particulars of a month-to-month apartment agreement may vary, changes in the terms of the agreement will usually involve giving written notice at least 30 days in advance. This is true for the tenant as well as the landlord. Other details, like the deposit amount and what constitutes appropriate use are spelled out in a short-term rental agreement just as they are in a longer term lease.
A month-to-month apartment rental is a flexible arrangement for the renter, but flexibility comes at a price. The one exception is when a standard-lease term expires. It isn't uncommon for a standard lease of a year or more to convert to a month-to-month arrangement after the lease term has elapsed. If rent is relatively flat in the area, making it unlikely that it'll go up, this type of month-to-month rental doesn't cost more but can be a flexible option for the renter who is contemplating a change of residence in the future.