They've been around Texas, California, and other western states long before they were even American territory. You've probably learned in school that the Spanish held a lot of colonies in North America beginning from the 1500's. They didn't mind intermarry with the Native Americans as much as the English thus they produced a large numbers of "Mestizos" offsprings. After the United States took control of these territories after the Mexican-American War, many of them remained and some were granted full citizenship. (I recently learned that Billy the Kid often intermingled with the Hispanics when he first arrived in New Mexico.)

Other tidbits:

Puerto Ricans became American citizens in 1917, so they became free to move in the mainland United States. A large numbers of Cuban refugees came to the US after the Cuban Revolution and after Castro took power (Desi Arnaz was one of them).

In the early part of the 20th Century, Hispanic women bright dresses were often seen selling chili in San Antonio. They were called Chili Queens.