The Guardians of the Galaxy-2008 takes place in the canon Earth-616 Marvel timeline. They are only connected to the original group tangentially by a meeting with Vance Astro from another unknown temporal continuity. The group that will be seen in the Marvel Cinematic Universe (Earth-19999) will likely have slightly different origins and capabilities.
The Guardian of the Galaxy have a complicated pedigree. The first set came from an alternate universe Earth-691. They were all the last survivors of a war in our solar system against an alien reptilian species called the Badoon.
The Guardians are active in the 31st century in an alternate time-line of the Marvel Universe (Earth-691). The original members of the team include Major Vance Astro, an astronaut from the 20th century Earth who spends a thousand years travelling to Alpha Centauri in suspended animation. He is also the future-counterpart of the hero Vance Astrovik, now called Justice. Martinex T'Naga, a crystalline being from Pluto; Captain Charlie-27, a soldier from Jupiter; and Yondu Udonta, a blue-skinned "noble savage" from Beta Centauri IV comprise the original team.
During the course of the war against the Badoon, the team recruit two more members - Starhawk and Nikki - and travel back in time and encounter several of the heroes of 20th century Earth, including Captain America and the Thing (Marvel Two-In-One #4-5, 1974).
I liked this set of Guardians but they weren't able to live up to their title as protectors of the galaxy at first. Since they came from an alternative future, they were not considered part of the canon Marvel Earth-616.
And here is where it gets complicated.
A team of stellar heroes including Star-Lord, Adam Warlock, Rocket Raccoon, Drax the Destroyer, Gamora, Phyla-Vell, Groot and Mantis. These heroes will become the Guardians of the Galaxy of Earth-616. But they will not take on that name until they meet a semi-amnesiac who will identify himself as Vance Astro, Major Victory of the Guardians of the Galaxy.
This group of heroes were already engaged in proactively protecting the galaxy from threats. They had not taken a name but were already appearing in a series of connected comics series including Annihilation: Prologue and Annihilation: Conquest. The link takes you to the entry at the Scifi.StackExchange listing the comics for that series.
This as-yet-unnamed team meet a and discover he is a time-line displaced version of the hero who led the original Guardians of the Galaxy from the Earth-691 timeline mentioned earlier. It is after meeting Astro, that they take on the name and become the Earth-616 Guardians of the Galaxy.
In the aftermath of the Phalanx invasion of the Kree, Star-Lord decides to form a team of interstellar heroes that will be proactive in protecting the galaxy, rather than reacting to crises as they happen. To this end, he recruits Adam Warlock, Drax the Destroyer, Gamora, Phyla-Vell (the new Quasar), Rocket Raccoon, and Groot, with Mantis as support staff. On the recommendation of their ally, Nova, the group establishes a base of operations on the space station Knowhere, which possesses a teleportation system with near-universal range. An intelligent, telepathic dog named Cosmo is Knowhere's chief of security and works closely with the new team.
Making things more complicated is the fact that every one of the new Guardians already has a long pedigree and sometimes had a very different appearance since the last time they had been seen. As a matter of fact, most of these heroes were part of short-lived, and considered relatively-unsuccessful-financially series from the 1960's and early 1970's.
Adam Warlock: A genetically designed human with cosmic powers engineered by a group of scientists on Earth. Superhumanly strong, fast, and able to absorb cosmic energy from the environment. For a time, he possessed the Soul Gem. Every time he dies or approaches death, he is able to enter into a regenerative cocoon which gives him a new appearance and new powers. His powers resemble the manipulation of cosmic forces and can resemble magical abilities.
Drax the Destroyer: Currently a green-skinned, bald male covered with red tatoos. He was once a human being who died and was returned to life as a living weapon to destroy Thanos. For a time he possessed Thor-level strength and was nearly indestructible. He dies and is resurrected even more powerful but the death had damaged his psyche. Superpowerful and child-like, he was more a danger to others than his target and was exiled to the Microverse. Recently he has reappeared and while much less physically powerful, his mind has returned to normal. His prowess in hand to hand is excellent and is still has extraordinary durability.
Gamora: Created by Thanos to be the equal of the future self of Adam Warlock called the Magus for which she was designed to slay. She has been both genetically and cybernetically enhanced, has an enhanced healing factor, and trained in martial arts techniques from across the galaxy by Thanos. She has also been trained with almost any common weapon in the Milky Way galaxy and has been trained to defeat opponents whose strength may exceed hers by thousands of times. For a time, she possessed a dagger which could kill anyone even a god-like being like the Magus or Thanos. It is unknown if she still possesses that weapon. She is considered one of the most proficient humanoid martial artist ever and has been called "deadliest assassin in the galaxy."
Star-Lord: Born Peter Quill of Earth, he was a human who was given powers, a living starship and he adventured thorough space as the self-styled Star-Lord. He reappears in the recent titles, sans Ship and special weapons. Now he is a mercenary, tactician, leader, soldier and bastard. His trademark was the using of twin Kree submachine-guns simultaneously. Star-lord was outfitted with a Kree issued heat-dampening-espionage-battle suit, which became the hallmark look for the Guardians of the Galaxy, battle helmet and a universal translator, all of which he still uses. His battle helmet analyses strategy data, can improve vision and regulate oxygen when in space.
Phyla-Vell: She is the genetic daughter of the Kree Captain Mar-vell and Titanian Eternal Elysius. Her genetic legacy gave her superhuman strength, energy projection and the power of flight. She also acts like an "energy sponge," absorbing any energy attacks directed at her and returning them as energy blasts. She has cosmic awareness and is a proficient fighter. For a time, she possessed the Quantum Bands of the hero Quasar (Wendell Vaughn) and gained access to a host of photo-kinetic and energy manipulation abilities. Losing them, she becomes an agent of Oblivion and gains other unknown powers.
Groot: another character from the sixties Groot first appeared in Tales to Astonish vol. 1 #13 (November 1960), and was created by Stan Lee, Jack Kirby, and Dick Ayers. He is a mobile plant with superhuman strength and durability. As long as a sprig of him remains he can seemingly return to himself after he spends time regenerating. Calm, durable, wise, and patient, Groot is the heart of this team.
Rocket Raccoon: Rocket Raccoon possesses the normal attributes of an Earth raccoon, including an acute sense of smell, sight, hearing and touch. He is an accomplished starship pilot, an excellent marksman with the two laser pistols he carries as well as having an affinity for heavy weapons. He's also an excellent military tactician and leader, attributes that help him take charge of the Guardians of the Galaxy when Starlord is unavailable.