Screening a potential tenant is the first step to finding the right one. If you accept a person into the rental home on a first impression, gut instinct, or anything other subjective reason, you're opening yourself up for a headache. If you choose one person over another without any solid reasoning behind it, you may find that the applicant denied claims discrimination. It's always good to have a steady process in place to avoid even the appearance of discrimination and you should always stand by that process. Another problem that occurs when you do not go through a proper background check is that you have no clear view of the person living in your property. You are, ultimately, responsible for what happens, so if you allow them in and they turn the unit into a meth lab, you'll likely be stuck with that bill and cleanup.
When you first accept a tenant into your unit as a renter it is a good practice to lay to rules out for them in an easy-to-understand format. This way you know that everyone is on the same page. Putting these rules into writing is an even better practice, so that no misunderstandings will occur. You may refer back to the document if the tenant has a question later on or has broken a rule.
Once the tenant is settled, you'll want to make sure that you are both responsive to their request and responsible to follow through. You'll keep good tenants longer if they know that they can rely on you to fix anything that breaks in the unit. You'll also want to perform regular inspections to make sure that the unit is being kept up and that no rules are being broken such as unwanted pets or illegal activities. Keep in mind, if a tenant has caused destruction to your property, they're probably going to be less likely to invite you in where you can see it. You'll want to make sure that the first time you see it isn't when they move out and have left you with the bill.
There are some infractions that will require you to begin an eviction process immediately. Others, though, you may want to work on. Check out BiggerPocket's tips on how to turn bad tenants into good ones here.