Chuck, I'll explain my understanding of it, although I have no scientific basis for the explaination. I just know it works this way so take it for what it's worth.
When you give the paper a pre-flash, you are changing the contrast of the paper, (and the possibilities are wide, since you can use any filter to expose your pre-flash exposure thru, or you can just use unfiltered light...which will be like a grade 2) and are giving it some density to work with during the main exposure. Of course, how much it changes depends on how much pre-flash you give it. Lets say if you exposed a print on a grade 1 1/2, and the contrast looks great, but you want some pre-flash (because you've determined that the pre and not the post flash will be better). And lets say you chose to do the pre flash on a grade 00 (because they are really blocked up. You could use a 1, or any filter for that matter, it just depends on the density of your highlights), because your highlights are the problem. So, you've changed the basic "grade" of the paper because you've "fogged" it with a flat exposure. When you go to make your main exposure, since you are starting with a flatter paper, you will need to change your contrast, made a #2, to make up for the paper being "flatter" to begin with. You will also need to change the time, since you are starting your main exposure with a paper that already has density on it.
Now when you post flash, and lets go with everything above...main exposure on a 1 1/2, you are basically "filling in" highlight areas with density...kind of like fill flash when shooting and you have a main light source and are using fill flash to fill in dark areas. This post flash can effect the shadow area, but usually it doesn't, unless you are giving it a substantial amount. You could dodge the shadows some if need be, but most of the time it isn't necessary.
Sometimes you'll need/want to do both, and then that throws a whole bunch more variables into the mix. Try to remember whats been done is the hardest part...especially at my age.
This is a simple explaination...I could write a book on the whole proceedure, and maybe I'll make a few samples one day and make a web page with them. However, its a lot of work and the possibilities are endless. As always, you are going to need to try it out and pay attention to the results. After a few years, you'll get the hang of it

For me it comes pretty easy and I can see after 1 test strip and 1 full test print, what I need and how much.
BTY, I use a seperate enlarger so I can adjust the height (for different print sizes), bellow amount (I always throw the flash light out of focus even though I am going to stop down quite a bit and bring some of it back in focus), f-stop and exposure.
Hope this helps.