How did the people in ancient times carve such beautiful designs into these stones, such as the cylinder seals of Sumeria, or the ancient Egyptian scarabs? What process and tools did they use? If anyone here can provide an answer, or refer me to a website or book, I would be very thankful. I am looking for a detailed description of the actual process.
I've not looked into the Near Eastern examples you bring up, but if you are interested in small stone engraving in Greek antiquity, you might take a look at:
Boardman, J. (2001) Greek Gems and Finger Rings: Early Bronze Age to Late Classical (2nd ed.). London.
Plantzos, D. (1999) Hellenistic Engraved Gems. Oxford.
Of these, Boardman is a good chronological survey, with much discussion of the origins of Greek gem carving (which is heavily indebted to Egyptian scarab carving). Plantzos is more narrowly focused on Hellentistic gems, but has the technical discussions you're looking for.
My recollection from Plantzos is that Greek gem carving was done by specialist artists who occasionally signed their names on the gems. The work was done by hand with extremely fine chisels and hand drills. There's no evidence for any sort of magnifying gear. During the actual carving process, the engraving would have been heavily obscured by detritus, so probably the artists worked in stages, washing the stone to see how the carving was coming on, then working more or less blind for a bit, then washing and checking again. The entire process was extraordinarily labor intensive, with P. estimating several months of man-hours for the highest quality of gem.