You remove the cap and rotor. There is a screw in a slotted hole that holds the points assembly to the plate. Underneath the points also have a pin that engages the plate so when you loosen the screw it will pivot closer or farther from the cam. There is usually a little notch in the base and in the points on one side that you can fit a slotted screwdriver in to pivot them around easier than freehand.
To actually measure the gap you bump the starter or turn the engine by hand so that the points are at their maximum opening. This make take a few tries to get it to stop in the right spot. You then use the proper feeler gauge and the above process to get the proper gap. You then put it all back together, start it up and hopefully hook up a dwell meter to confirm you got the correct setting. If not you take it back apart and make a slight adjustment till you get it in the range. The gap method is only a guide and is only fairly accurate on new points. Checking it with a dwell meter is the most accurate since that is what the coil sees and if the dwell is not in its optimum range the coil will not operate at its peak efficiency. Dwell is not like timing where you can just play with it and maybe get it better, more dwell does not equal more spark. The most annoying part of points is after you put some miles on and they wear you should do this adjustment all over again. Now days I think the quality of replacement points seems to be crap so you will have to re adjust or replace even sooner. This is why most of us have done some sort of conversion to electronic like Petronix, DS2, or DUI. The GM V8's actually had a little hatch that opened in the side and you used a small alllen wrench to make the adjustment while the engine was running. That was pretty sweet because it was quick. Its not too bad on other engines once you are used to it. You just get a feel for it and know how much to move them to get it where you want. You also learn when its close enough so you dont spend time getting it back to as good as you had it to start with. Also when you have a dwell meter hooked up rev the engine and the reading should stay steady. If it jumps around a lot you have worn bushings in the distributor and the shaft is bouncing around which causes the dwell to drift which means you are not getting 100% from your system.