Explain how ordinary individuals can influence the Texas government. 500 words

Since you need enough information on which to base a 500-word essay, this answer aims both to provide you with the necessary information and to direct you to sources that can help you locate additional information.
Several components of the instruction you provide first need to be defined or clarified, especially “ordinary individuals” and “Texas government.”
Anyone living in the state of Texas could consider themselves an “ordinary individual.” It seems that your assignment is asking you to look at people who are not involved with organizations that are paid to promote special interests (or lobbies) or at people who are government representatives, such as congressional representatives. Furthermore, an “ordinary individual” need not be a US citizen or legal resident of Texas, but could be someone who is living temporarily in the state. Many opportunities to influence government are limited to citizens.
“Influence” is often considered the domain of lobbies, as they seek to shape the course of government action, such as a vote regarding a particular law.
In addition, here we will assume that “Texas government” means elected representatives and the work-force of the state of Texas, including counties or municipalities, rather than US congressional representatives from Texas.
The listing for the government of Texas on an “official website of the United States government,” usa.gov, is one good place to look for accurate information. “The official website for the State of Texas,” texas.gov will also be useful.
The US constitution guarantees many rights to US citizens that are germane to the ways that individuals can influence government. The First Amendment's provisions of freedom of speech, assembly, and petition are especially important in this regard. All Americans have the right to speak freely; this include oral speech, written speech, and modes of expression. All Americans also have freedom to assemble peacefully. In combination, these two freedoms support important ways that ordinary people can try to influence the government. Among the ways they could do so is by speaking with a representative of the state government, such as by making a phone call or sending an email or text to the governor. The official state website provides a hashtag, “#GetEngaged,” to facilitate communication.
The freedom to petition the government means that an individual can approach a government representative with an idea about how the government should be changed. The most typical way that this plays out is through efforts to have a new law passed or to amend (change) an existing law, which begins with ideas that lead to the introduction of a bill. This requires individuals to interact with local level government representatives, who collectively make up the people’s representation. The Texas legislature also has an official website for the Texas Legislature Online (TLO), capitol.texas.gov, which includes information on the status of bills. Individual involvement could take the form of attending a public hearing as a bill makes its way through committees or is discussed in either chamber of the legislature.
For US citizens who are at least 18 years old, voting is one of the key ways to influence the government. The State website for the Secretary of State’s office has voter information, and it provides a link to another site, votetexas.gov, that includes even more information. In Texas, advance registration is required 30 days before an election.
Even for those not old enough to vote, following the government’s activities is important to shaping an individual’s future involvement. The TLO site links to the site for “Kids House” activities with the House of Representatives, https://kids.house.texas.gov/
Finally, learning about a government's activities is crucial to understanding what it is doing. The Texas legislature broadcasts can be accessed through a link on the TLO site.
https://www.usa.gov/state-government/texas