Is there a suffix that is "-miş"? Because I see it at the end of some words and don´t really know what it stands for 

It gives the meaning that it is said tho have happened.

Kitabı okumuş : He says that he has read the book.

Ders çalışmış : He claims that he has studied his lesson.

It gives the meaning that it is said tho have happened.

Kitabı okumuş : He says that he has read the book.

Ders çalışmış : He claims that he has studied his lesson.

Could you elaborate further on when to use muş vs miş?

-muş has a few different uses.

This is a good link:

http://blog.demturkishcenter.com/how-to-use-the-mis-suffix-in-turkish/

signifies past tense and is usually used if what has happened in the past was not actually seen by the person talking.

the link above explains it in great detail