You'll face quite a laundry list of requirements for a Secret Service agent job (source). After all, you'll be protecting the president or vice president of the United States; to say they're a little careful about who they give this job to is like saying Lebron James is kind of good at basketball.
You've got to be a United States citizen between twenty-one and thirty-seven years old when you're appointed (sorry dad, you're too old). You'll need either a bachelor's degree from an accredited educational institution, or three years work experience in the law enforcement or criminal investigative fields.
Within this experience, you must have demonstrated knowledge and proper application of criminal violation laws, or a combination of education and applicable experience. For some reason, the government doesn't want to hire anyone who can't prove they know what they're talking about.
Being able to see well is more important than you might think in this gig. You must have uncorrected vision of 20/60 binocular or better, correctable to 20/20 in each eye. If you've had some corrective eye surgeries, you might be accepted if you can pass certain visual tests. You'll also have to be in top-notch health and physical condition, as some of your work, such as protective detail duties, could get quite strenuous.
Your application process will be as detailed as your protection itinerary. You'll have to pass a medical exam, a drug screening test, a polygraph test, and some type of written examination—although maybe that's a secret, too (source).
Then comes the fun part: the six-to-nine-month background investigation, where the agency interviews your family members, friends, neighbors, coworkers, ex-coworkers, former neighbors, ex-former-neighbors, maybe an ex-boyfriend or ex-girlfriend, and even your mail carrier.
What did you expect? This is the Secret Service—it's their job to be thorough.