In short, in high school Chemistry it is mostly memorization when it comes to acid strength. It isn't till at least Organic Chemistry in college that you start to learn how to determine acid strength by structure. There aren't too many strong acids. A general rule of thumb is if it isn't HCl, HI, HBr, HNO3, H2SO4, or HClO4 then most likely it isn't a strong acid. There are a few exceptions, but not too many that you will see.
Most strong bases you will encounter have xOH where x is usually an alkali ion or a alkaline ion.