Earth originally had one Lantern: Hal Jordan.
Guy Gardner was selected as Hal's backup. When Abin Sur was dying, both Guy and Hal were qualified to be Green Lanterns; Hal got the ring because he was closer. (from Green Lantern v2, #59)
When Guy was injured such that he couldn't serve as a backup, John Stewart became the back-up GL. (from Green Lantern v@, #87)
Guy recovered and served as the backup when Hal was unavailable on at least one occasion after John became the backup backup. Guy was injured further when his power battery exploded; in fact, he was presumed dead, but had actually been tossed into the Phantom Zone. He was eventually retrieved from the Zone, but the combination of his time there, his first injury, and the power battery explosion left him with brain damage, and comatose. (circa Green Lantern v2, #116-123)
This left John as the backup Lantern again. When Hal decided to retire from being Green Lantern, John took over the role. (circa Green Lantern v2, #182).
This lead into DC's Crisis on Infinite Earths crossover. During this story, one group of Guardians brought Guy out of his coma and gave him a ring and a mission. His personality was radically different (presumably due to the brain damage), and he took to considering himself the one true Green Lantern. Hal got his ring back at that time as well. The events of that story lead to the Guardians leaving the universe, and the GLs being allowed to stay where they wished. For a time, not only were Hal, John, and Guy all Green Lanterns, but 5 other GLs came to Earth and worked with them. Well, with Hal and John; with his personality issues, Guy did not work well with this little Earth GL Corps. (circa Green Lantern v2, 193-200; Green Lantern Corps v1, 201-224)
A lot happens from there for all three characters, but little that's relevant to the question for a while.
- The GL Corps was basically disbanded for a while, when most of their rings were destroyed (though all three of the above kept theirs).
- Hal helped work to rebuild the GL Corps, splitting his time between Earth and space, until his home town was destroyed (in the Death of Superman storyline and following); then, he went kinda berserk and killed or maimed a lot of the Lanterns. He ended up destroying the Corps, caused Zero Hour, and then sacrificed himself to restore the sun during the Final Night storyline.
- John technically became a Guardian for a short while, then (following Hal's destruction of the Corps) joined another intergalactic peace-keeping organization, the Darkstars.
- Guy wound up getting involved with the Justice League when it reformed following the Crisis. Eventually, he got booted from the Lanterns for a while. During that time he first acquired Sinestro's yellow ring, then a different power set altogether.
Following Hal's destruction of the Corps, Kyle Rayner of Earth was found by a Guardian - Ganthet - and given the last ring. He served as the only Lantern for years, before helping to refound the Corps. During the rebuilding period, Kyle convinces John Stewart to accept a ring again.
Eventually, Jordan was restored to life (and cleansed of an alien entity which had been responsible for his evil actions). During this, Guy lost his other power set, and was given a ring back as well, leaving all four of Earth's Lanterns alive and active again.
In recent times, the Corps has doubled in size: each sector now has two Lanterns. Officially, Hal Jordan is GL 2814.1 and John Stewart is GL 2814.2 (Earth being in Sector 2814). Guy and Kyle are members of the Green Lantern Honor Guard - described as Lanterns with no sector. The Honor Guard are 3rd in line as decision makers on Oa, and are free to act in any Sector they choose.
Other members of the Corps have been known to complain about the number of 'Earthens' represented in the Corps - most species have only a single active member at a time (if that many).