I just asked my two-year-old grandson to "help" with my kegs, so I think I can explain it pretty well!
"Force carbing" simply means to carb the beer with co2, instead of "natural" carbonation (priming sugar).
Some people do that by shaking/rocking the keg, or by giving more pressure to the keg than is needed. That often results in overcarbed or foamy beer, though, so I wouldn't do that.
The easiest way to carb your beer is to siphon it to the keg, give it a blast of co2, pull the pressure relief valve, and then give it another blast. That makes sure to purge out the 02, and also helps to ensure the lid is seated. I spray star-san over the lid/posts to make sure there are no leaks.
Then, put it in the kegerator (which is set at 40 degrees) at 12 psi for about 10 days. Pour a beer, and it should be carbed up.
There isn't really any such thing as a "serving" pressure and a "carbonation" pressure, as a properly balanced system stays the same all the time. I have 6 kegs hooked up. Can you imagine changing the pressures to drink/carbonate? It would drive me crazy! The beer would go flat over time at a lower pressure, but turning it up and down may cause foaming.
If you can't wait 7-10 days to drink the beer, then one way around that is to set the regulator for 30 psi for 36 hours, then purge and reset to 12 psi. That hurries the carbonation up, but doesn't shake/roll the keg and cause foaming or overcarbonation. Another risk with shaking/rolling is to have beer back up into the gas line and ruining the regulator!
It's really easy to force carb. The easiest way is to "set it and forget it" at 12 psi at 40 degrees, or whatever a carbonation chart says is right for the temperature of the beer. http://www.kegerators.com/carbonation-table.php