基本概念

There are two kinds of lease

1.  fixed term lease, a written lease of fixed terms, such as from 7/1/XX to 6/30/XX+1.   Like gqc asked, if you signed the lease and mailed to the tenant, the tenant could sign any time and make the rental "fixed term lease".  Then your options are limited by the written lease. 

2.  tenant at will, if there is no written lease, there is still a lease existing, but it is treated as tenant at will, basically month-to-month.  

To end a tenant at will lease, depend on state law, either landlord or tenant has to inform the other party a month ahead in writing, then the lease is ended. 

To be sure of correct procedure for your state, please Google "XX state month to month lease" or "XX state tenant at will".