Take a cruise. This is the easiest opportunity to swim with stingrays.
Make sure your cruise goes to the Caribbean, specifically Grand Cayman Island. The Cayman Islands are home to something called Stingray City, home to many tame stingrays.
Book your stingray excursion through your cruise line. Usually, you book excursions when you get on the ship. Book early to ensure that not all the spots are taken before you register.
Learn to swim. Stingray City is on a sandbar, so you can stand with your head above water, but you'll have to swim from the boat to the sandbar.
Wear a bathing suit and water shoes on the day of the trip. Make sure to apply sunscreen because not only will the sun be coming from above, but it'll reflect off of the water. You'll be out on the boat for quite a while and you don't want to get sunburned.
Listen to the instructions. Your tour guides are experienced and can explain how to walk and interact with the stingrays. If you listen to everything they say and follow all of their directions, you'll be perfectly safe.