Need direction on getting a good tenant

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I just purchased my first duplex!  The upper unit is occupied, but I need to find a tenant for the lower unit.  On other properties, I have always had a manager help with this, so I don't have any experience doing this myself.  Can anyone walk me through how to find and vet for a really good tenant?  How to advertise?  Logistics of the application process?  Background/ credit check process?  Any tenant scoring rubrics?  Thanks in advance!!