Make a checklist of the condition of the property and any furnishings when you move in. (Most properties will provide you with an inventory and condition form).Tenants agree to pay their rent in the form of a personal check, a cashier's check, or a money order made out to the Landlord. 4. Applicant's name (as listed on proof of identification). Applicant's former last name (if applicable). E-mail. How to fill out a residential lease application in Texas? Any other information that will be used to fill out the lease. They must then move out of the rental. It is important to know what you are agreeing to and what your rights are when renting property. Remember to read your lease before signing it.