I screen all my tenants. First, I call all their personal references and places(s) of employment. It has been a work of evolution over the years to learn what questions to ask since sometimes people can be deceitful. There are also questions you cannot legally ask so make sure you are aware of these.
I also pay an outside firm to run complete state and federal background checks. These are mostly involving criminal, court, financial and out of state items. A separate form for the potential tenant is needed for them to sign that allows the checks to be made.