Texas shares an international border with Mexico as well as a 600 mile coastline. It is bordered on the north by the state of Oklahoma, on the west by the state of New Mexico, and on the east by the states of Arkansas and Louisiana. As a state of the United States, all visa and passport rules of the USA apply.
By plane
Texas has several international airports, including the Dallas/Fort Worth International Airport DFW, the largest and busiest airport in Texas and 4th busiest airport in the United States. It is a major airline hub and is relatively cheap to fly into. Houston's George Bush Intercontinental Airport IAH is also a major hub and has the most international connections in the state. Other major airports can be found in, Austin, and San Antonio, though almost every reasonably sized city in the state is served by some kind of air transportation.
By car
Texas is well-served from other points in the U.S. by the United States Interstate Highway system, the quality and condition of which is generally very good. There are many roads which cross into Texas from Mexico, most notably in McAllen, Brownsville, Laredo and El Paso. Due to the enormous amount of traffic from Mexico and Central America, Laredo is the country's largest inland port, and wait times at this and all border stations can often be tremendous. In all, Texas boasts over 72,000 miles of state and federal highways.
If you are not a U.S. citizen and you are driving into the U.S. from Mexico, you must have a visa or valid permit beforehand, as they are not issued at the bridges across the Rio Grande. If you are a U.S. citizen, you must present a passport to customs at the border crossings to re-enter the United States. Otherwise, your vacation in Mexico just got longer!