According to The Chicago Manual of Style, 16th edition, sections 7.16-7.21, the apostrophe is required in all such cases, except where the noun is either plural in form but singular in meaning (the example politics’ true meaning is given), or in the case of “for … sake” expressions, for the sake of euphony (the example for goodness’ sake is given).
With specific regard to skipping the final s after the apostrophe in names like your son’s, Chicago states, “Though easy to apply and economical, such usage disregards pronunciation and is therefore not recommended by Chicago.”
The primary reason for the confusion so many have on this issue is that the common practice was formerly to leave off the second s.
So, properly written, for example, the athletic footwear that belong to your son would be James’s sneakers. However, if you are reading a document written many years ago and come across the old usage without the s, it was considered correct in that time and place.
A note: my post above refers only to apostrophes used in possessives. There are, of course, dozens of other apostrophe rules, and associated exceptions, like that cited by core_dump (which is actually permitted under Chicago 7.14) for other circumstances. For the OP, your best bet might be to visit your local library and, for your own ongoing personal reference, copy pages 351 to 358 of the 16th edition Chicago Manual and select the rules for your wall chart from among those you find most likely to confuse.
There is no one clear universal rule that all authorities will agree on. There have been threads on this in the past and I’ve collected the results in my Unofficial FAQ. The poster linked by two different members above is a great summary and includes the advice on this point that either is acceptable as long as you’re consistent.
I have read Fowlers, Chicago Manual, the CP Stylebook, and other authorities! I know what they say… as I said in my post. I want personal opinion. If I wrote James’ would you think I was elitist, or if I wrote “James’s” would you think I was unedumacated?