What are some home remedies for a stye in the eye?

Heat: Apply heat to the eyelid and wash it with an eyelid cleaner. There are several available commercially, but dilute baby shampoo will also work. Heat a wet wash cloth in the microwave for a short time (15 sec) and if not too hot ( you do not want to damage your skin and the skin on the eyelids is very thin) apply to the sty. The clean it with lid scrubs. Some of these need antibiotics.

Warm compresses: Warm compresses (wash cloth with hot water and hold it on the stye for 5-10 minutes, reheating as needed), or surgical incision and drainage, or steroid have been the only effective treatments demonstrated get rid of a stye. A stye is due to the orifice of an oil gland (mebomian gland) in the eyelid margin becoming inflamed, and not an infection, so antibiotics are not indicated.