Primary Elections
Primary Elections are put on by the two major political parties (Republican and Democratic) on the first Tuesday of even-numbered years. The Hays County Elections Administrator works with the parties to conduct holding and tallying of the vote. All candidates of those two parties go through a filing process to get on the ballot, choose a campaign treasurer, and provide regular reports of campaign donations and expenditures.
The winners of each race face off with the winner for that race in the other party (if one ran) in the General Election which is held in November. Races with more than two primary candidates may require a runoff election to decide the winner.
Other political parties (such as Green Party and Libertarian) hold nominating conventions to choose their candidates to run for various offices.
Texas primaries are OPEN, meaning voters do not register as a member of a party and can vote in either primary or attend a party convention. But once they vote in that primary or convention, they may not change parties during the primary runoff or convention.
Some counties have such an imbalance between the parties that the primary election results in choosing the next office holder, whether the minority party fields a candidate or not. More info
here.