The first step is to provide the tenant with a written notice to vacate the premises. This notice must comply with Texas law regarding its content and delivery method. 

There are three main types of notices: Notice to Vacate for non-payment of rent, Notice to Cure or Quit for lease violations, and Notice to Vacate without specifying a reason for month-to-month leases. 

The response time depends on the type of notice given. For non-payment of rent, the tenant typically has 3 days to pay or vacate. For lease violations, they have 3 to 10 days to correct the violation or vacate. 

If the tenant does not leave the property voluntarily after the notice period expires, the landlord can file a Forcible Entry and Detainer (eviction) lawsuit in the Justice of the Peace court. 

The landlord must file a petition and pay the required fees at the Justice of the Peace court that has jurisdiction over the property.