Polyatomic ions form part of the language, or nomenclature of chemistry. We name these groups of atoms so because of their high tendencies to stick together and behave as one.

Common polyatomic ions, in order of electrovalence, then in pseudo-alphabetical order, with related ions adjacent:

Now, I'm not sure how anyone memorizes these, but the following pattern may help. For almost any infix X, the number of oxygen atoms in the molecule decreases one by one, creating this order of names:

perXate
Xate
Xite
hypoXite
Note that most of the time, this pattern only manifests partially.

I would appreciate any advice from people who actually know chemistry well; it's not my field.

Sources:
http://www2.austin.cc.tx.us/rvsmthsc/chem/chem-Some.html
http://www.chemistry.wustl.edu/EduDev/LabTutorials/PeriodicProperties/Ions/ions.html
http://scidiv.bcc.ctc.edu/wv/4/0004-009-Polyatomicions.html
http://home.earthlink.net/~ssbeaton/addlinfo/polyions.html

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