There are several basic qualifications that you must meet before applying. You must be under the age of 40 (unless you have had previous law enforcement experience), be a U.S. citizen, have a valid driver's license, be fluent in Spanish or display a willingness to learn, and pass a fitness test. The Patrol will look to see if you have any past arrests, convictions, dismissals from past jobs, or if you have taken illegal drugs or have a substance abuse problem. Although your job involves the confiscation of drugs, they are not looking for "drug experts" here. They would prefer that you only be able to identify them and recognize their properties. No firsthand knowledge required.
When you apply to the Border Patrol, they will conduct a polygraph test, fitness test, background check, and a medical test. It takes six months to pass all of their tests. Once you have received a letter that you have been accepted, you go to the U.S. Border Patrol Academy in New Mexico. The training lasts for 55 days, or 94 days if you come in without being fluent in Spanish. That extra time is not a punishment, by the way; it just takes that long to learn Spanish.
While at the academy, you will undergo physical training and a crash course in law. The academy will also teach you how to use firearms. You are then stationed somewhere and begin your probationary period. The idea is to not foul up or accidentally shoot a fellow agent during that time, so you can become a full-fledged BTA.