The process

Section 25.19 of the Texas Property Tax Code requires appraisers in each District to send out Appraisal notice to residential property owners by April 1st (or as soon as practically possible otherwise).
These notice are technically only required if the property value or the exemption status has changed however in practice all homeowners receive this notice. The notice informs the homeowners of the Districts appraised value for the current tax year as well as details of an exemptions applied to the property and any homestead cap.

The Appraisal Value is determined using the Mass Market Appraisal process. I explain this process in further detail here (hyperlink)

Homeowners have until April 30th (or 30 days after the notice of appraisal is delivered) to file a protest. In filing a protest you do not have to provide evidence. The form requests that you indicate on what basis you are appealing the valuation. These include:

Market Valuation

My house is not worth that much

Unequal Appraisal

My house is appraised for more than my (similar) neighbor