The basic word for "home" in Spanish is "hogar." The phrase "My home" is "mi hogar." However, "hogar" is not always used if you want to say "home" because sentences can translate differently from English into Spanish.
A common phrase is "mi casa," which means "my house." However, "casa" is commonly used for "home." For example, "Estoy en casa" translates to "I'm home."
If you want to say "I'm going home," say "voy a mi casa." Casa is considered appropriate when you speak about the home inside the house, while hogar is used for the building. For example, if you want to say, "in my house we love each other," you can say "en mi hogar nos amamos." Hogar is also used for the word household, so household products is "productos del hogar," and for a fireplace or hearth.