Apostrophes are used to show that letters are missing or to indicate possession. �Can't' is short for �cannot', so the apostrophe stands for the missing letters �n' and �o'.
In this phrase...'the dog's tail'...the apostrophe shows that the tail belongs to one dog as it is between the 'g' and the 's'. The same idea applies here...'the dogs' tails'...only this time, there are two or more dogs involved. In such cases, the apostrophe comes after the �s' of �dogs'.
When you have an irregular noun - that is, one that doesn't make its plural by adding �s', such as man/men or child/children - the apostrophe is put at the end of the basic plural word and not after the possessive �s'. For example, you should write...'the men's cars' or �the children's school'.
Always avoid what is known as the greengrocer's apostrophe, which is wrongly used to create plurals as in "Apple's �1.00 for a pound!" instead of "Apples �1.00 for a pound!" Not only greengrocers do this, of course, but they do seem to be particularly prone to it.
Not exactly a mnemonic, I agree, but it does explain how the apostrophe works.