Additional resources Chandler mentioned on the WFAA Yallitics podcast with Jason Whitely & Jason Wheeler:
Follow these steps:
Watch the video below
Print and fill out this Homestead exemption form for Texas. This is the statewide version of the form. Some counties supply their own.
Make a copy of your driver's license showing your new address
Mail the form and a copy of your driver's license to the appraisal district (mailing addresses are below the video)
This video covers everything you need to know about Homestead Exemptions in Texas:
Where to mail your property tax homestead exemption forms: