The regular old way of doing the initial grinding.
The way that a spherical surface is generated with two pieces of glass is with the differential abrasion that happens when you take two pieces of any material and rub one on the other with some abrasive material between them. As you overhang the one piece over the other, the edges of the piece beneath and the center area of the piece on top wear away faster than other areas of the material as there is more of the weight on those areas than the average of the whole surface. Towards this end, we will want to keep one piece of glass on the top (the mirror piece) and one piece on the bottom (the tool piece) and grind them together. As far as making a spherical surface, remember that the only type of surface that can be produced where both surfaces are in full contact with each other in all directions and rotations is a spherical surface. The radius that you grind can be any radius (a radius of infinity, i.e. flat, is still a radius) but it is the only pair of surfaces that can mate with each other and allow for motion of one surface over the other. So lets get going with the process.
Start by putting the piece of glass selected as being the tool on the platform that you have built to hold the tool from moving all over the place and sprinkle a large pinch (ask your wife, the cook, if you don't know what a pinch is) of the largest grinding compound that you got in the kit (80 grit or so) and then pour a puddle of water about 2" in diameter on the mirror. Place the piece of glass selected as the mirror on top and start pushing the glass back and forth. You will immediately hear a loud raspy grinding noise. That is perfectly normal and is the grit chipping little pieces of the glass off of the two pieces of glass. The grinding sound will quickly start getting quieter and at some point (rather quickly in the beginning), will get quieter. You will also notice that the black of the silicon carbide will start getting gray. This is the mixing of the scrap glass particles which are white in color with the black silicon carbide. I usually stop grinding when the color turns a medium gray and quickly clean off the mirror and tool of the grit and glass. You can do this by a quick wipe of your hand on each surface and rinse you hand in the bucket of water that you are keeping nearby. You don't need to clean off every little bit of the grit and glass fragments as you're going to make a lot more of them real quickly. I might also note that much of the grit will just be washed off of the face of the mirror so feel free to pick it up and put it back on the face again. I also keep the grit that gets washed off and clean it with a few swishes of the water to clean out the glass which floats better than the carbide and reuse it when finishing up the coarse grit.
After you have started grinding the motion that you want is a W type of stroke which overhangs on one side of the tool by as much as half the diameter of the tool. The minimum is a slight overhang. This is the initial curve generation stroke and will be used only with the coarse grit to carve out the basic hole in the mirror for the radius of curvature that is desired. As you do the grinding, turn the mirror in your hand. This turning of the mirror will be a constant thing that you will do for every stroke that you do. The mirror should turn fast enough so that in about 15 strokes or so, it makes a full turn around and is facing the same way again. The stroke speed for the coarse grit down to the middle grits can be as quick as you desire but don't wear your arms out or you will have to stop and after a while, you won't want to do the work as it will be tiring to you. After you do every couple of strokes you should also rotate the work point on the tool, whether rotating the tool or moving around the barrel so that you are constantly grinding on new areas of the tool. Experienced workers just do a slow shuffle around their barrel instead of standing in one place and then moving to a new place after a while.
If you are grinding a long focal length mirror, the overhang doesn't need to be as much after you have started as what it would be for a shorter focal length mirror because you don't need to grind as deep a hole. This is something that experienced grinders know by approximation as to how far over to put the mirror in order to get the depth as fast as possible. The less experienced grinder can make a curve of something longer than the radius that they want (use a radius bar to generate the curve) on a piece of plywood or other thin wood or plastic and measure the radius of what you are generating as you go along. The center of the mirror will be the first place that the hole in the mirror will be seen. If the radius is too short, spending more time towards the center of the mirror over the center of the tool will cause the radius to expand to fill the entire surface of the mirror without digging into the center as much.
While grinding, one of the things to be careful of is to not allow the mirror to fall off of full contact with the tool. This rocking motion places an exremely high pressure on the edge of the tool and will cause a chip or sliver to form and probably fall off of the tool and at worst, you can even break the mirror in half with this pressure. A chip off of the tool looks a lot worse than it really is but it is still not a good thing as you will have to stop work and get the glass slivers off of the workplace (and then bevel the tool so that it doesn't happen again) before you get a nasty cut from the very sharp edge of one of the slivers. Handle the slivers very carefully and throw them away in a very safe manner as they are sharper than a very sharp knife.
When you get finished with a grinding session during the rough grinding, thoroughly wash off everything into the bucket. Pour off most of the water and then pour some more water in and swish the grit and glass in the bottom around a bit to wash out the grit from the glass. The grit falls to the bottom a lot faster than the glass and thus you can recover a lot of the grit that you pushed off of the tool while grinding. Wash and pour off the water several times until the grit in the bottom is pretty black and then you can take and use that grit first when you start the next session. This will allow you to be able to easily grind any mirror without running out of grit. Only the coarse grit should be treated this way as the smaller grits need to be clean in order not to get scratches on the mirror.