Legally, the standard lease states that you can post a for rent sign and begin showing to prospective new tenants, 60 days prior to the end of the lease (if you list it for sale- you have 90 days). You should ask the tenant to clean up, most tenants will. I use to manage rental property. We always asked that the tenant leave the residence if possible when showing. If listing for sale, maybe offer a $100 credit monthly for keeping house clean and easily accessible. The tenant has the right to be there though. We also always assured the tenant when listing the house, that appointments will be made.
To answer the question at hand, the best method is by appointment only. Try to show when tenants is at work.
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