How do you cure a stye?

Prepare a hot/very warm towel or a gauze that is slightly wet. Put that on to the stye 7 or 8 times a day. After that your stye should be gone. In case it isn't, you should contact a medical professional.
First and foremost do NOT try to pop the stye. That is the worst thing to do for it as it will get infected (worse).

You have two options, you can see your doctor and ask them to prescribe you with medicated eye drops that will help clear up the infection. Or, you can use a hot compress (warm wet wash cloth) for 5-10 mins, 3-4 times a day. Make sure that when you use a warm cloth you get a CLEAN one every time. This will help keep from spreading new bacteria. Avoid any make-up or moisturizer in that area. Try really hard not to touch. It should clear up on its own in a few days. If not I strong suggest going to see your doctor.