The first Green Lantern was Alan Scott, who made his initial appearance in All-American Comics #16 in 1940. His power ring was made of a magical artifact called the Starheart--its only weakness was that it was completely powerless against anything made of wood (which is quite a drawback when you're fighting the evil Dr. Tree). He was a founding member of the Justice Society of America back in the 1940s and recently (due to various comic book crises, he's still relatively young) gave up his ring. However, he's used the ring for so long that the energy of the Starheart still resides within him, allowing him to pull all kinds of power-ring stunts without actually having a power ring. Nowadays, he goes by the name "Sentinel".
Earth's next Green Lantern was a test pilot named Hal Jordan. He was given his power ring by a dying member of the Green Lantern Corps (see Habakkuk's excellent writeup below for a summary of the Corps). His first appearance was in Showcase #22 in 1959. The only weakness of Jordan's ring was that it was powerless against anything colored yellow (again, a big problem when facing the villainy of Captain Pee). For many years, Jordan was the only Green Lantern from Earth, but in later years, Guy Gardner and John Stewart were also given power rings. However, Hal was widely considered to be the greatest member of the Green Lantern Corps ever. But when his hometown was destroyed, Hal went nuts, destroyed the Corps and most of the Guardians, and tried to remake the universe as the supervillain Parallax.
The last of the Guardians traveled to Earth with the last power ring (and it was the best one, since it was no longer powerless against yellow things). He arrived in an alley and gave the ring to the first guy he saw--luckily, it was generally nice-guy and freelance artist Kyle Rayner, instead of someone like the Joker. Rayner helped defeat Parallax and continued as the only Green Lantern. Later, when he got hold of some more power rings, Rayner appointed his girlfriend, Jennifer Hayden (the green-skinned and babelicious daughter of Alan Scott), as the newest Green Lantern. Kyle also became, briefly, a god when his ring got supercharged, but he gave up most of that power so he could re-create Oa, the Guardians, and the Central Power Battery.


Check this out http://www.dcuguide.com/Who/Sentinel_Bio.htm