Testing telescope mirrors
To grind a mirror is relatively easy, except for the final stages of figuring. The whole grinding and polishing process the mirror and tool have a tendency to converge to a spherical shape. After all, this is the only shape where full contact is possible while the surfaces are moved. High or low regions will wear faster and slower respectively, until the sphere is attained. The stroke that will get you there is the infamous standard stroke; approximately 1/3 diameter stroke length with only a little sideways movement.
Knife edge testing
Analysis of the surface profile is done by means of a testing device, which can be made with fairly basic tools. The easiest is the knife edge test, invented by Leon Foucault (aka Foucault test). A point or slit shaped lightsource at radius of curvature (twice the focal length) is reflected by the mirror under test. The image of the lightsource is then analyzed by means of a knife edge.
A second method which is fairly easy to implement by amateurs is a Bath common-path interferometer. The basic idea is to split a laser beam, use one to illuminate the mirror and the other as a reference beam. The reference beam is also reflected from the mirror, and takes approximately the same route as the illuminating beam. Upon return both are mixed and from the interference pattern the surface shape can be deduced. There are two good information sources for starting with this way of testing: a very informative wiki and the yahoo interferometry group.
Finally, I have upgraded the floppy drive tester base with a set of professional translator stages. This is now my generic test platform, used to carry all sorts of test heads.