There really isn't a good way to explain how the number of oxygens determines the suffix on your anion's name. Nitrate (NO32-) has three oxygens as does chlorate (ClO3-) but both phosphate (PO43-) and sulfate (SO42-) have four oxygens.
The best answer I can tell you is that you have to memorize the names polyatomic anions which end in -ate. Unfortunately, there is no systematic relationship between number of oxygens in the anion and its name. However, once you know that chlorate is ClO3-, you can find the structures of chlorite, hypochlorite, and perchlorate by following the rules outlined in the wikipedia page I posted earlier.