The apostrophe is used in two ways:
1. To indicate missing letters. For example: "do not" can be shortened to "don't"; "she would have" can be shortened to "she'd've"; "Shakin' Stevens" was the stage name of a singer, the apostrophe indicates a missing "g".
2. To indicate possession. For example: "the teeth of the fierce dog" can be expressed as "the fierce dog's teeth"; "the husbands of the ladies" can be expressed as "the ladies' husbands".
The apostrophe does not indicate a plural. Some people do use an apostrophe for the plural of an abbreviation -- for example, "Would you like to see my huge collection of Shakin' Stevens CD's?" -- but many people regard this as incorrect: it should be "CDs". (The jury is still out on that one.)
Notice the distinction:
I saw the boys yesterday. (This is a plural. No apostrophe.)
Is that the boy's book? (Possession. Apostrophe.)
It gets confusing with "it's" and "its", and it's a very common error even among native speakers. "It's" is short for "it is" or "it has"; "Its" means "of it". You might think that, because it indicates possession, it should have an apostrophe, but the rule is different here. "Dog", "ladies", "CD" and "boy" are all nouns. "It" and "its" are personal pronouns. You don't write "hi's money"; it's "his money".
Many native speakers do often write an apostrophe where none belongs. This is sometimes called the "greengrocers' apostrophe" because it's a common sight in greengrocers and on market stalls. They will often write "potato's" when it should be "potatoes" or "mango's" when it should be "mangos". For some reason, words ending in "o" seem to give people especially big problems.