What is the simple rule of thumb to help children remember where apostrophes go?
In English grammar, as far as I know, apostrophes are most commonly used for contractions or possessives. As for remembering where apostrophes go in contractions, the way I was taught to remember it was that the apostrophe replaces the missing letter when two different words are put together to create one word.
Ex. should not
As you can see above, the "o" in "not" was removed and replaced with an apostrophe, thus turning "should not" to "shouldn't".
I find that the letter that is substituted with an apostrophe is usually a vowel. Below are a few more examples.
Ex. it is
Ex. can not
(An alternate version of "can't" is also "cannot")
Ex. could not have
(In this slightly longer example, you remove the "h" and "a" in "have" instead of just the vowel. The same generally holds true in most three-word contractions.)
Apostrophes can also be used for possessives and the images below are probably able to explain it better than I could and they provide a visual as well!
For the full poster on proper apostrophe usage, you can use this link :)