My earliest "publishing" was a newsletter written and produced by myself and a colleague at school around 1953. To produce multiple copies, we typed the text onto "skins" also called stencils (using a typewriter with no ribbon to cut the skin). These were a thin rubbery material that fitted into a hand-operated printing machine. After applying printers ink appropriately and filling the paper feed, one could turn the handle to roll off copies of that page. We had a rather ancient mechanical Gestetner machine which was temperamental but we coaxed it to do the necessary. See here . If non-typewriter text was required (banner headline, crossword square, ..) then a pointed metal stylus could be used to draw directly on the skin.
When I started research in 1963 as a graduate student, publication and communication were very different from today. There was no e-mail, internet, mobile phone or personal computer. Post was the main channel, with TELEX (a way to send text messages to selected institutions) as an option in some cases. Telephone was available, but not readily accessible to graduate students.
One could learn of other people's work by reading the Scientific Journals in the library or by looking at "preprints". Preprints were typed versions of the manuscript of a research paper which were sent to selected institutions and individuals by post much before the paper was published in a journal. Russian language journals were subsequently translated and published in the US -- it saved time if one could understand the original and, luckily, the equations were easily readable. I made an attempt to teach myself Russian - with some success. Around 1966, when I was a post-doc at Rutherford Laboratory - they allowed me to have an hour one-on-one with a native Russian speaker every week. I always assumed this service was some left-over of spy activities.
When you wanted to publish a paper, first you wrote it in legible hand-writing and then gave it to a secretary to type. They were not impressed if you subsequently wanted to change anything. Mostly secretaries left spaces for you to insert the equations by hand. Scientific typewriters did exist - some with two interchangeable carriages - but were not popular with secretaries. The advent of electrical "golf-ball" typewriters with easily interchangeable "golf-balls" made this a bit easier for secretaries. They tended not to know the names of symbols (mathematical and Greek) so conversation with them to explain exactly which symbol was required in the text was curious.
When a paper required figures, these were drawn on graph paper and then turned into technical drawings (Indian ink on tracing paper) either by the drawing office or you did it yourself. I quite liked doing my own figures, since one could produce a nice looking result with the stencils, pens, drawing tools,.. which was pleasing for someone like myself with "messy" handwriting. The original figures were sent in with the typescript when submitting a paper to a journal. Copies could usually be made by the drawing office - some with a blue tinge: the original "blue-prints".
To make copies of the typescript, one relied on carbon copies, some of which could be rather "murky". Around 1965 better quality photocopying machines became available but they were heavily rationed to graduate students. As late as 1974, I was still using photocopies that relied on special paper and gave poor quality copies.
When, after negotiation with referees and editor, a paper was accepted for publication, one would later receive the proofs. These were to be corrected by hand using an arcane set of symbols. In due course (often over a year from submitting the original manuscript) the Journal volume would arrive with the paper in it. One also received (or else paid for) a certain number of reprints. These were printed just as in the Journal and could be given to interested parties (they were often needed for job applications also). A stack of reprints on a shelf by your desk was a sign of "impact" in those days.