In punctuation-speak, a point is a period. Here's a tip on using points.
It's cumbersome and unnecessary to use points in such abbreviations as CIA (name of an agency), UAE (name of a country), ILGWU (name of a union), UNESCO (name of an international organization - and pronounced as a word), NW (name of a compass point - and written out as a single word northwest, except in Britain and sometimes in Canada), and so on. Points should be avoided even with the initials of people, unless part of the name is spelled out: JFK, J.F. Kennedy; Old GS was at the tournament, and Bill C. was there but Bill G. wasn't.
There are a few initial-type abbreviations that do require points. U.S. always has points, perhaps to avoid momentary confusion with the word us, but USA rarely does. U.K. (United Kingdom) usually has points, perhaps to avoid the infelicitous result of trying to pronounce the abbreviation as a word. The abbreviations of academic and professional degrees - B.A., D.D.S. - usually have points; some of them, of course, are not made up entirely of initials: Ph.D., Litt.D. A few degree abbreviations are used informally to refer to people, usually without points: He is a CPA; MBAs are taking over the water-skiing industry. Initial-type abbreviations of state names have points - N.Y., R.I. - but not when they are used with ZIP codes: NY 10010. The ZIP code style was established by the U.S. Postal Service.
Other abbreviations almost always have points. Saint is abbreviated St.; Mister is abbreviated Mr.; Lieutenant Commander is abbreviated Lt. Cmdr. Exceptions are mainly very common abbreviations for units of measure. The preferred forms are still lb., oz., ft., and so on, but lb, oz, and ft are commonly seen and are accepted - unlike in for inch and gal for gallon, which can too easily be misunderstood. Points are not used with metric abbreviations: cc, mm, kg, and so on.
Enough exceptions to this rule exist to make a dictionary essential in doubtful cases, but the general principle of the rule should be sufficient for abbreviations not found in the dictionary.