How do you memorize the general polyatomic ions?

My teacher told me that if you memorize cyanate, acetate, carbonate, nitrate, chlorate, permanganate, phosphate, sulfate, chromate, oxalate, dichromate, cyanide, hydroxide, and ammonium that you could then build all the other polyatomic ions off of those, but I can't figure out why some have 2 oxygen, some have 3, and some have 4, and I can't remember the charge either. If you have any advice, please help!