Break the tab between the two halves of the receptacle on the hot (brass) side.

Power feed:
BLACK WIRE: To the top brass screw of the receptacle and the white wire (remarked) going to the switch.
WHITE WIRE: To the neutral (silver side).

Switch feed:
BLACK WIRE: To the bottom hot (brass) screw.
WHITE WIRE: To the Black wire of the feed.

Switch itself:
BLACK WIRE: One screw
WHITE WIRE (remarked): the other screw

(of course I've omitted all the grounds which should be connected together and to the box (if metal) and the grounding screw on the devices).

#1) that was a very confusing description.
#2) I typed in "switched receptacle" to google, and here is the first link

Here is a link that might be useful: Diagram

I concur, the only difference in my description and the picture they gave is they made the bottom unswitched and mine describes the top unswitched (and it matters not really which way you do it).

One thing not pointed out in the drawing, while it's permissible to use a white jacketed conductor to feed the switch (but not the return), it is no longer allowed to not remark it when doing so.

Although I have a passing familiarity with split receptacles, I never really thought much about them. Is this the only acceptable way to wire them or can two circuits be used breaking two tabs? That might mean two grounds going to the same box, right?

Two circuit can be used with a shared netural. Only break the hot(gold) tab.
or
Two cricuits can be used with two hots and two neutrals. Break both tabs tie all grounds from both circuits together.

The way shown is the common use. Another way is to wire an Multiwire branch circuit so that the top and the bottom are on opposite legs. This is common in Canadian kitchens, but not so much in the US.
Running distinct branch circuits to the same yoke has it's own grounding issues.

Thanks for elaborating on the basic theme.