I need some people to explain this about Spanish to me! Por favor!?

When someone is to refer of something as theirs, how do they do that correctly in Spanish! I think if someone were to say,"That is my dog." they might would say something similar to,"Estas es mi perro."? If I'm wrong, which I probably am please tell me how to construct that sentence and others like that. Also I know there are other forms of "my" in Spanish such as "mi", "mio", and maybe "mia". Please explain to me when these words are used in proper Spanish grammar, because I have no idea where and when they are supposed to be used! Thank you in advance!!!