How were the figures in old pre-TeX research papers and books created? If you see old pre-TeX-era classic research papers, technical articles and books the figures still look pretty good. They seem to be hand drawn but with some components of computerization.

For example see this CRAY-1 document: http://bitsavers.org/pdf/cray/CRAY-1/CRAY-1_Brochure_1975.pdf

How were these figures created? What tools did folks use to create and then place them into the paper or book?
This depends on the age in which the papers were developed. In the computer age there have been graphics programs going back to somewhere in the 1950's so it is possible that they were created on a computer. Possibly using vector graphics. 

But note that the machines on which early programs ran were large and expensive. 

Earlier than that, and overlapping with the computer age, artists were employed by publishers to create graphics using the same sort of tools that architects and "draftsmen" used. The French Curve was common and every student in a course in mechanics (physics) had one to help prepare homework. Actually artists may still be employed, but they tend to use computer tools now, rather than manual ones. 

Math and physics undergraduates needed to be quite adept at graphing functions by hand, but these were a bit too crude for publishing. Hence artists. 

To extend it a bit, even in the 1970's mathematics papers needing formulae and equations with any complexity were prepared by hand by skilled typists using specialized typewriters. The special symbols, hundreds of them, were on individual wands that were inserted into the typewriter under the striker. The glyph was struck and then the wand removed so the next one could be inserted. The typists worked from hand written papers prepared by the author. 

For publishing, pages were prepared in sets of, say, 16 and printed using something like the lithographic process. The 16 (or whatever) pages printed together became a "signature" and these were prepared and the sewn together to make a volume. High quality books often still use sewn signatures, which you can see by looking at a closed book from the top or bottom - the "spine". You can also see the threads used to sew the signatures. See Book Binding for example.