OK, let's cut to the chase: the apostrophe is good for the following, and ONLY the following:
It is a punctuation mark which has two main functions:
It marks omissions:
e.g., do not: don't
e.g., it is: it's
e.g., is not: isn't
e.g., there is: there's
e.g., was not: wasn't
e.g., would not : wouldn't
e.g., can not: can't
Hopefully you readers can get the gist ad infinitum.
The apostrophe also assists in marking the possessives of singular nouns:
e.g., the girl's book
e.g., the peacock's feathers
If you have more than one girl or peacock, then:
...the girls' book
...the peacocks' feathers
Do not use the apostrophe if you are writing "its", as in "The racehorse gave its best."
If you do, it will say: The racehorse gave it's best. (The racehorse gave it is best.)
Good grief, this is not difficult to comprehend. This punctuation business has been going on for years! Decades! Centuries! But for some reason, the past decade or more has shown that punctuation rules have dropped so low as to make normal reading even of newspapers and internet dreary reading for one who adheres to normal grammar and punctuation.
A couple of years ago I emailed a Wall Street Journal advertiser who misused the words "its" and "it's". I received a not-very-nice email in return. But I suspect, given this writer's tone on reply, that I was not the only editor in the country who had written him that day.
So here is my rant.
Get with it, you English writers!
This is not difficult.
Follow the ding-dong rules.