The style of pad I like to do is a separate upholstery unit, in my mind, it makes for a much cleaner look on the bike and is a lot easier to remove for underseat access than the snap cover type. This type is shown on my personal bike, yeah, I actually ride on the parts I make!
The first step in my process is to make a fiberglass base pan for the pad, I use an original seat for the mold, and wax it so the glass doesn't stick to it, a couple layers of chopped mat is stiff enough for this purpose. When it's all cured, I remove it and trim to the shape I want, I use templates for the seats I make all the time, it saves some measuring and marking time and ensures everyone's getting exactly what's in the picture.
Next I drill out holes for 1/8" rivets along the edge of the pan, I find rivets work best to hold down the material without starting tears in it.
Depending on the firmness desired, I make a base layer of at least 1/2" of high density closed cell foam, similar to yoga mats, or those floor covers for work areas. Spray adhesive or contact cement work well to hold the foam to the fiberglass base. The next layer(s) of foam should be a lower density type that adds a bit of cushion and lets the sewn material move a bit, it looks better than using only high density foam throughout.
With the foam layers adhered to the fiberglass base, I use a bandsaw, or a hand razor saw would work as well, to cut the foam using the edge of the fiberglass as a guide. This makes sure the foam is straight along the sides and won't make the covering look lumpy.
Next, and this is a very important step, (I've had people tell me some of the "really famous" builders don't do this and have problems with the covers tearing!), I cover the fiberglass edge in either a few layers of masking tape or gaffer tape. This keeps the abrasive fibers from rubbing holes in the vinyl covering... surprised that some people never think that far ahead.
tomorrow - sewing the cover