Pictured is a Neumann mastering lathe. It makes the master disc from which 'real' records are pressed-in vinyl! This is state-of-the-art 70's tech, made in Germany by the same company that made all those great tube mics you can't afford to buy now. There is other gear involved in making a master-equalizers, limiters, and other sound processing gear, plus a console that adjusts the levels for the disc. Neumann also made these, but most mastering houses preferred to build their own. I've added a pic of a Scully lathe also. It was another popular system for mastering vinyl records.
The process goes like this: The master recording-done on analog tape-is played back thru (usually) ultra-fine-tuned speakers, and adjustments to the sound are made so the sound will transfer properly to the disc. This is the art of the process. Some fairly major adjustments to the sound can be made at this time for artistic or technical reasons. The goal is to have as 'perfect' sounding recording as possible that will play correctly on the customers turntable. There are rules of physics that are involved in this process that cannot be broken or the disc will not play on your record player. As you can see, the disc has a finite amount of space, and you must cut grooves in the disc that do not touch, or cut too deep or shallow on the surface. You also want the record to play back as loud as possible, and with little distortion. Oh-and don't forget time: the longer the playing time, the less room you have to accomplish all this. Most albums of the era were about 18:00 a side, maybe a bit more. This was enough time to get the sound loud enough and with enough bass and treble to sound reasonably "Hi-Fi" as they used to say. This format was not very forgiving of errors. There were standards for making master discs that could not be 'out of spec' or the master would be rejected by the factory (pressing plant) that made the finished records.
The job of the mastering engineer-the one who performed this transfer from tape to a disc- had to know all these rules, have great ears to make adjustments for the sound, and be very fast with their hands to make all the changes needed between songs on an LP album! When the transfer to the disc was finished, the engineer had to check every bit of the finished disc with a microscope to make sure the grooves were correctly spaced. The usual width of a groove was 2.0 to 2.5 millimeters for an LP, hence the name 'microgrooves'.
My description of this procedure is quite elementary, as I don't want to get you zoned out and glassy-eyed with a lot of technical jargon. Just giving you the basic steps on what is/was involved in this process. Betcha didn't know it was so complicated, did ya?
One more thing: CDs, MP3's and your Ipod may be the current technology, very easy to use and transportable, but none of these sound nearly as good as a well made high-quality vinyl record. I would also add the bonus of all the great art work that was done for the front and back covers of LP records. A little paper picture in a CD case (and the small print) is no match for a 12" x 12" canvas of art that the LP cover was.