Heinlein's The Puppet Masters, published in 1951, involved three space-stations orbiting Earth. I am curious to know which was the earliest science-fiction which involves space-stations. Furthermore, which was the first one to use the term space-station?
I wouldn't mind an answer addressing short stories, novels, and film. For completeness :)
There are two separate questions here, concerning the origin of the concept and the term.
The earliest science-fiction story about a space station is Edward Everett Hale's 1869 "The Brick Moon" with its 1870 sequel "Life in the Brick Moon" (a combined edition from 1872 is available as a Project Gutenberg etext), but that doesn't answer your question because "The Brick Moon" is only a novella and you asked for a novel. The Puppet Masters (1951) is certainly not the earliest one, because part of Heinlein's 1948 novel Space Cadet is set on a space station. This calls for more research.
If you don't insist on novel length, but you want examples from modern science fiction (so the space stations will be constructed of metals and plastics instead of bricks), a famous early example is "The Jameson Satellite" by Neil R. Jones, first published in Amazing Stories, July 1931:
He had then soliloquized upon the possibility of preserving the human body in its state of death until the end of all earthly time—to that day when the earth would return to the sun from which it had sprung. Quite suddenly one day he had conceived the answer to the puzzling problem which obsessed his mind, leaving him awed with its wild, uncanny potentialities.
He would have his body shot into space enclosed in a rocket to become a satellite of the earth as long as the earth continued to exist. He reasoned logically. Any material substance, whether of organic or inorganic origin, cast into the depths of space would exist indefinitely. He had visualized his dead body enclosed in a rocket flying off into the illimitable maw of space. He would remain in perfect preservation, while on earth millions of generations of mankind would live and die, their bodies to molder into the dust of the forgotten past. He would exist in this unchanged manner until that day when mankind, beneath a cooling sun, should fade out forever in the chill, thin atmosphere of a dying world. And still his body would remain intact and as perfect in its rocket container as on that day of the far-gone past when it had left the earth to be hurled out on its career. What a magnificent idea!
You can read the whole story at Project Gutenberg.
But that's just an orbiting mausoleum. If you want a space station with a livelier crew, there's Frank K. Kelly's obscure novelette "Famine on Mars" from Astounding Stories, September 1934, available at the Internet Archive. Notwithstanding the title of the story, the action takes place on a manned (and womanned and Martianned) space station in Earth orbit:
The station seemed to hang in space like a giant's lantern, put here to light the void between the Earth and her satellite moon; no comparison could have been more true; without the constant ebb and flow of beam signals, relayed from Earth to Mars and back again, there could have been no traffic in the void.
As for the term "space station", the earliest citation in the OED is from an editorial essay by Hugo Gernsback in Air Wonder Stories, April 1930:
It might be asked: what useful purpose would be served by converting a space-flyer into a permanent, rapidly-revolving satellite of the earth in this manner? Professor Hermann Oberth, perhaps the greatest authority on interplanetary space, points out many uses for such revolving ‘space stations’, as he calls them. A better word, perhaps, would be ‘revolving space observatories’.
There is a 1929 citation, from editorial matter in Gernsback's Science Wonder Stories, for the form "spatial station". This does not answer your question, which asks for the first use in a science fiction novel.
So far, the earliest example I've found of the term "space station" in a work of fiction (unfortunately not a novel) is in Manly Wade Wellman's short story "Space Station No. 1", first published in the October 10, 1936 issue of Argosy, reprinted in Famous Fantastic Mysteries, September-October 1939 which is available at The Internet Archive:
In its time Space Station No. 1 was unique in the solar system and probably the universe, for, of all the worlds that swung around the sun, it alone was a creation of mortal engineers and mechanics, built of materials artificially prepared, shaped and joined, for civilized purposes and profit.
Without it the Martio-Terrestrial League's Jovian colonies might well have failed at the start. Jupiter's moons abounded in valuable minerals, offered broad lands for development and settlement by emigrants, but they were almost too far away. Only once in two years were Mars and Jupiter in conjunction, close enough for liners and freighters to ply between. A few days thus, then the planets drifted apart on their orbits, the gap widening to an impossible distance for two years more.
Wherefore the League's experts planned and built Space Station No. 1, to circle the sun along Mars' orbit, but on the far side of the sun from Mars. Old Sol's gravity carried the synthetic planetoid in approximate position, as the current of a whirlpool carries a chip of wood in an endless circle. Occasional rocket blasts kept the station exactly where it should be. Thus, when the planet was in opposition and at its farthest from Jupiter, the station was at its closest, a half-way house for the refueling of Jupiter-bound ships from Earth and Mars. Supplies and other relief could reach the colonies once each year instead of once each two years.
Kurd Laßwitz' novel "Auf zwei Planeten" published in 1898 has a space station in a geo-stationary orbit (over the north pole, which I think is not actually possible). The book also features a xerox-like procedure to make quick copies, wide-scale use of solar power ("why waste your fortune when you can live happily off the interest collected") and synthetic foodstuffs.
The two planets referred to in the title are Earth and Mars; the space station is constructed by the Martians and in the course of the story turns from a research station into a bridgehead for the martian colonization effort. Build around the same themes "Auf zwei Planeten" is pretty much the opposite of "War of the Worlds" (Laßwitz deemed Wells to be an cynic) - also a parable on empire-building (Martians stood in for the Germans in this case) but altogether ending on a more happy note - the Martians are not defeated by the faceless forces of evolution but, being a civilized society, find their way back to their enlightened mores and accept humans as equals. A wonderful book if you happen to be interested in german philosophical idealism (perhaps a bit long-winded if you're not).
As far as I recall the book does not use the term space station. I don't know if this is the earliest use of the concept but it seems earlier than the other answers.
Who would've guessed that Wikipedia has an article on that topic? There, Venus Equilateral is mentioned:
Venus Equilateral Relay Station, from the 1940s Venus Equilateral series by George O. Smith, is a communications hub set in Venus' L4 point.
Indeed, the book search indicates that the term 'space station' was used there (the Google Books search links to the 1980s reprint)
Also, Google's Ngram search for space station shows 1940 as the earliest entry (depends on the corpus you search). Unfortunately, you can't access which work represents a specific data point. I actually like the mid-50s space station hype :)
For perhaps the first example of a space station portrayed in a fairly "realistic" way (unlike the Brick Moon books mentioned by user14111), it's mentioned in this sf-encyclopedia entry that rocketry pioneer Konstantin Tsiolkovsky published a story in 1920 titled "Vne zemli", later translated into English as "Out of the Earth" (available in The Call of the Cosmos), which featured "the first detailed and thoroughly scientific treatment" of a space station. The article describes the story as "a semifictionalized didactic speculation; it deals with free fall, space greenhouses for growing food, communication via space mirrors, and artificial Gravity effected by spinning the station on its axis". A more detailed summary can be found on p. 748 of Science-Fiction, the Early Years which can be seen on google books here, the summary starts with "(d)" a little more than halfway down the left-hand column. The entry describes it as:
A short novel describing the first venture into space. Containing long expositional passages, it is the first important hard interplanetary novel since Jules Verne's lunar voyage.
There is some descriptions of the preparations, and finally of the ship that takes them into space, and the "space greenhouse" they build once in orbit:
Work is now commenced on the master vessel. When finished it is about 325 feet long and spindle-shaped. ... The vessel functions perfectly, and the explorers put themselves into a hundred-minute orbit around the earth. The author describes the nature and function of space suits, the problems of weightlessness, and artificial gravity as obtained by rotating the ship. Once out in space for a considerable time, the men assemble a gigantic space greenhouse; it is about sixteen hundred feet long, seven feet wide, glazed, provided with suitable atmosphere, and fertilized with the excrements of the explorers. Without gravity to hold them down and with perpetual sunlight, plants grow with fantastic rapidity, even including dwarf fruit trees. By the time that the provisions the explorers brought with them are exhausted, the greenhouse is fully functioning, providing them with a luxuriance of delicious food for years. The explorers communicate with earth by means of space mirrors, reporting what they have accomplished. Since they offer a solution to the problem of over-population, their attainments are highly regarded, and a system of similar space colonies is set up. Volunteers are carefully screened and conditioned to low air pressure and weak gravity, and in a very short time thousands of space greenhouses, with living quarters attached, are orbiting around the earth. Most such greenhouses hold about four hundred people, with suitable plant space. Many are linked with communicating passages and air locks, so that there is an interchange of population and the beginnings of a space culture.
