From Quake Wiki
Quake is not a game well-known for having a deep, well-executed story. The plot as included in the .txt file that can be found in the root directory of a fresh install contains a few paragraphs that give the game a very rough background that helps to explain the sudden shifts between modern bases, medieval and strange Netherworldian environments. As the player progresses through the game, additional passages are presented to them at the end of each episode, and upon finishing the game, having collected all four Runes and defeated Shub-Niggurath.
This is the text that can be found in the manual.txt that is included in every install of Quake.
You get the phone call at 4 a.m. By 5:30 you're in the secret installation. The commander explains tersely, "It's about the Slipgate device. Once we perfect these, we'll be able to use them to transport people and cargo from one place to another instantly.
"An enemy codenamed Quake, is using his own slipgates to insert death squads inside our bases to kill, steal, and kidnap..
"The hell of it is we have no idea where he's from. Our top scientists think Quake's not from Earth, but another dimension. They say Quake's preparing to unleash his real army, whatever that is.
"You're our best man. This is Operation Counterstrike and you're in charge. Find Quake, and stop him ... or it ... You have full authority to requisition anything you need. If the eggheads are right, all our lives are expendable.."
Prelude to Destruction
While scouting the neighborhood, you hear shots back at the base Damn, that Quake bastard works fast! He heard about Operation Counterstrike, and hit first. Racing back, you see the place is overrun. You are almost certainly the only survivor. Operation Counterstrike is over. Except for you.
You know that the heart of the installation holds a Slipgate. Since Quake's killers came through, it is still set to his dimension. You can use it to get loose in his hometown. Maybe you can get to the asshole personally. You pump a round into your shotgun, and get moving.
The Dimension of the Doomed
After taking the first Rune and defeating Chthon, the player is rewarded with the following text.
As the corpse of the monstrous entity Chthon sinks back into the lava whence it rose, you grip the Rune of Earth Magic tightly. Now that you have conquered the Dimension of the Doomed, realm of Earth Magic, you are ready to complete your task. A Rune of magic power lies at the end of each haunted land of Quake. Go forth, seek the totality of the four Runes!
The Realm of Black Magic
Once the player makes it out of the brutal final sequence of the Dismal Oubliette with the second Rune, the player is shown the following text.
The Rune of Black Magic throbs evilly in your hand and whispers dark thoughts into your brain. You learn the inmost lore of the Hell-Mother; Shub-Niggurath! You now know that she is behind all the terrible plotting which has led to so much death and horror. But she is not inviolate! Armed with this Rune, you realize that once all four Runes are combined, the gate to Shub-Niggurath's Pit will open, and you can face the Witch-Goddess herself in her frightful otherworld cathedral.
Once the player escapes with the third Rune from the Chambers of Torment, they are shown the following message.
The charred viscera of diabolic horrors bubble viscously as you seize the Rune of Hell Magic. Its heat scorches your hand, and its terrible secrets blight your mind. Gathering the shreds of your courage, you shake the devil's shackles from your soul, and become ever more hard and determined to destroy the hideous creatures whose mere existence threatens the souls and psyches of all the population of Earth.
The Elderworld ends with the player battling a group of vores in a tense battle, before grabbing the final Rune and escaping. Upon doing so, the following message is shown.
Despite the awful might of the Elder World, you have achieved the Rune of Elder Magic, capstone of all types of arcane wisdom. Beyond good and evil, beyond life and death, the Rune pulsates, heavy with import. Patient and potent, the Elder Being Shub-Niggurath weaves her dire plans to clear off all life from the Earth, and bring her own foul offspring to our world! For all the dwellers in these nightmare dimensions are her descendants! Once all Runes of magic power are united, the energy behind them will blast open the Gateway to Shub-Niggurath, and you can travel there to foil the Hell-Mother's plots in person.
All Runes collected
After collecting the all four runes, the player is shown the following text.
Now, you have all four Runes. You sense tremendous invisible forces moving to unseal ancient barriers. Shub-Niggurath had hoped to use the Runes Herself to clear off the Earth, but now instead, you will use them to enter her home and confront her as an avatar of avenging Earth-life. If you defeat her, you will be remembered forever as the savior of the planet. If she conquers, it will be as if you had never been born.
After killing Shub-Niggurath at the end of the game, the final congratulations message is displayed.
Congratulations and well done! You have beaten the hideous Shub-Niggurath, and her hundreds of ugly changelings and monsters. You have proven that your skill and your cunning are greater than nall the powers of Quake. You are the master now. Id Software salutes you.