"The supermarket is open today."
Translation:El supermercado está abierto hoy.
Ray, open is a readily changeable condition. It can change from open to closed, and back again, on a regular basis. Estar is usually used for these conditions, such as clean/dirty, well/sick, happy/sad, empty/full, etc.
Ser is usually used for describing the store's normal characteristics and qualities: es grande, es nuevo, es blanco, etc.