I wrote the contents of this post a few years ago to help me understand when apostrophes should and shouldn't be used. I offer it in case it's of help to others.

Let's start by forgetting any notion that the presence of the letter "s" automatically attracts an apostrophe. There are lots of cases where the "s" is fine without an apostrophe.

There are two reasons to use an apostrophe:

That's it. Apostrophes are never used for plurals.

Let's look at each reason in turn.

Possession
This is used when you want to say that something is possessed by or belongs to another thing, e.g. "My brother's walrus."

1. Singular nouns
Just add an apostrophe then an "s" to the end of the word that the thing belongs to. If you're talking about a hat that belongs to Geoff, write "Geoff's hat".

2. Other cases
But what happens when the word already has an "s" on the end? It depends why that "s" is there.

3. Plural nouns
Most plural words in English end in "s". If the word ends in an "s" because it is plural, add the apostrophe after the "s". For example:

(Tip: rearranging the sentences like this can help you to see what the word would be without the "s" sound at the end, so you know where you stand with adding the apostrophe.)

But watch out for words which are plural without an "s", like "men", "women" and "children". In this case, you can add an apostrophe and "s" in the same way as with singular nouns, to make, e.g. "men's", "women's" and "children's".

Words which just end in "s" anyway
Quite a few names just end in "s", like "James", "Jones" or "Cerys". In this case it would be confusing to add the apostrophe before the "s", because that creates confusion about what the name actually is (e.g. " Jame's" — is the name really "Jame"?).

In this case, treat the word the same as a singular noun (which it is!), and add an apostrophe and "s":

You may see these sorts of possessive written without the last "s", which is perfectly acceptable, but it may help you to remember the rules more consistently if you add it in, as we have here.

If it's a plural name and it's possessive, put the apostrophe after the "s", as you would do with any other plural noun. For example:

Contractions
An apostrophe is also used to indicate when a letter, or several letters, have been missed out of a word. Common examples include:

It can be hard to spot these, because they are spoken out in the contracted form. If you are aware of the full form, try to see if this would fit in the same context as you have used the contracted form, and, if so, spell it with an apostrophe.

For example, both of these work as sentences:

Or try these:

“Its" vs. "It's"
These often play the role of archenemy to the careful writer, but they illustrate very well the two reasons to use an apostrophe that we have been discussing here. One is a possessive, and one is a contraction.

Trying it out
But how would you know which to use in a sentence? Try sounding out your sentence with "its" and "it is" (the possessive and the contracted form expanded) and see which best fits.

For example, consider this sentence: "It is a very nice day today."

"It is" makes sense here, so if you substituted "It's" you would be using the contracted form. Another way to write the sentence is, "It's a very nice day today."

But consider this sentence: "Its sharp claws make the cat hard to love". You're not trying to say, "It is sharp claws . . . ", but rather that the claws belonging to the cat make it hard to love. No need for an apostrophe.

In summary: if you're trying to say "it is", use an apostrophe. If something belongs to it, don't use an apostrophe.

Comparing "its" with other possessives
We may think, after the first section, that "its" seems a bit unusual because it indicates possession but does not have an apostrophe with its "s". But consider these possessives:

These are known as "possessive pronouns" and they don't need apostrophes to indicate possession, because that's their whole job as words.

If it helps, try to think of "Its" as equivalent to "Yours" and "Theirs". None of them need apostrophes.

Summary
There are two main places to use an apostrophe:

Never use an apostrophe for a plural or just because there's an "s" there. Ask yourself whether the "s" is there to indicate possession or whether you've missed some letters out, and try to say the sentence a different way to see what the "s" sound is there for.

Enjoy using apostrophes ever more appropriately! And avoiding an apostrophe catastrophe.