You can't be a machinist without knowing how to properly measure your work. It sounds trivial, but it takes a while to develop a "feel" for proper measurement. In my case, the old machinist that took me under his wing way back in 1979 had

a fixation with measuring. He'd have me measure everything in sight with micrometer, vernier caliper, depth gauges, inside/outside calipers, etc.. I had to write down my figures. Being the neophyte that I was I thought he was crazy. He then re-checked all of my figures and proved to me how wrong my technique really was, and how much of a "touchy-feely" thing measuring really is. Olympic marksmen refer to this feel as "muscle memory" and it is something that can't be transferred through books of training courses -- you have to develop it by doing !! But hey, that's the pleasurable side of machining and why we do this stuff as a hobby anyway -- right ?

Besides the tools shown above (micrometers, squares, inside/outside calipers) you'll need some more specialized tools.

or fixture. The inside diameter measuring set will allow you to transfer measurements to your micrometer and dial caliper. A very handy tool, and is relatively cheap so you don't break the budget.