In reply to ROSP:
Second question first: as is evident from the responses, whether an upward-directional is part of the anchor is situational. Although I don't know out to categorize all possible situations, there are two basic considerations that cover a lot of the ground.
(1) Lifting the belayer will extract the anchor. This means the anchor is constructed entirely of nuts placed in vertical cracks (more about cams in a moment) . In this case, the party has to make a judgement call about how likely it is that the belayer could be dragged above the anchor by a fall and what the consequences of that would be. Personally, if my anchor is only nuts in vertical cracks, I'll usually try for an upward-directional piece, because predicting whether the belayer will be lifted is almost impossible, given the variables of rope and rock friction, possible weight mismatches, and the severity of the possible leader falls.
Some people argue that cams in vertical cracks will simply revolve and reorient for an upward pull. This is a big maybe; they might also be extracted by a 180 degree rotation, and I don't think anyone has a good way to make that judgement call. Still, in a pinch, you stand a better chance of the anchor in vertical cracks surviving an upward pull if the pieces are cams. That said, many people try to save their cams for the lead and won't have them in the anchor.
(2) A lifted belayer will hit something. The typical scenario is a belay right under a roof, which the belayer might hit with his or her head if lifted. An unconscious belayer is not a good thing. Making sure there is an effective directional in such situations is seems critical to me.
The first question is about how upward directionals are rigged. There are two basic options.
(1) The directional piece holds down the anchor pieces. With this option, the belayer can still be lifted a distance equal to twice the length of the belay tie-in.
(2) The directional piece holds down the belayer directly. This keeps the belayer from moving at all and so may stiffen the catch. (Note that according to tests by the CAI, only a very small amount of belayer lift actually reduces peak loads to the top piece.) This method is the one you want if there is a roof directly over the belayer's head, since it is primarily the belayer and not the anchor that is being protected.
Rigging. An upward directional piece usually has to be held under tension in order to be reliable for its task. So the free rope coming out of the anchor is run down to the directional and a clove hitch is used to tighten the connection to the anchor. For situation (1) that's it. For situation (2), the free rope from the upward directional is run back to the belayer and clipped to the rope loop tie-in loop or harness loop (pros and cons for each method; I prefer everything clipped to the rope tie-in loop).