This is the way I had to do it, which was kind of antiquated even for it's time ... but I'd turn the reel with my hands, manually, and listen for where you're going to make the cut. You then take a grease pensil and mark where the position is between the record / playback head.
Then, you put the tape on a block (splicing block) and slice it with a razor blade. You piece the stuff back together using a special kind of tape, and you'd do it on the back of the tape where there's no recording to mess with.
Yea, it was a pain in the ass, but there was a much greater level of satisfaction when you were actually able to make an edit work. You were kind of looked at as a magician.

Nowadays, it's just sort of ho-hum. Although I still think that, even today, there is a certain degree of value to being able to do a quality editing job, and to do it quickly / on the fly. Time is money, and if you can slice and dice / cut and paste in a timely and quality manner -- even on a computer -- those who are "on the clock" will appreciate it.