Don't worry, this post won't be nearly as bad as Wolverine: Origins. I promise!
I'm not going to go too deep into the character back stories in the comics. Today's going to be a little word light, because honestly, other people have done their homework already and I'm not going to copy from them. If you want a quick read with a little more detail, check out an article on the Hollywood Reporter.
Peter Quill aka Star-Lord
First Appearance: Marvel Preview #4, 1976
Star-Lord has his work cut out for him as the leader of an intergalactic band of misfits. He's the only human Guardian and has no "super" powers or enhanced abilities. Unless you count his sense of humor and wit.
First Appearance: Marvel Preview #7, 1976
I included The Incredible Hulk #271 (1982) instead of his first appearance because Rocket's not on that cover. The Hulk issue is his first color appearance. In addition to the enhanced senses you'd expect from a raccoon, Rocket is a great pilot and marksman...marksaminal? He is also known for his love of heavy ordnance.
First Appearance: Tales to Astonish #13, 1960
Groot was a bit different way back in 1960. I just read this story the other night in Rocket Raccoon & Groot: The Complete Collection. In it, Groot is an alien attacking the Earth. Pretty typical stuff for that era of giant monster comic stories. How did humanity stop nearly indestructible alien? Termites, they used termites.
First Appearance: Strange Tales #180, 1975
In Gamora's first appearance, she was known only as "female alien." She's since evolved into a gorgeous green-skinned woman that could kick Capt. Kirk's butt in a fist fight. She's said to be one of the most lethal martial artists in the Marvel Universe! She's also the adopted daughter of Thanos and the last living member of her species.
Drax the Destoyer
First Appearance: Iron Man #55, 1973
In the comic continuity, Drax is actually the soul of a human placed in an alien body for the sole purpose of destroying the mad titan Thanos. He was previously able to fly through space and shoot energy beams from his hands. More recently, he's lost most of his original powers except superhuman strength and has taken a liking to using knives in combat.
I fully expect their movie counterparts to have differing origins. But I'm really looking forward to seeing how James Gunn is going to pull these characters together into what he's called "Avengers in Space."