Good place to start is either with Emerald Dawn or Secret Origins. Emerald Dawn was essentially the GL version of Batman Year One or Superman: Man of Steel where they updated Hal Jordan's backstory, and was in canon until Geoff Johns released Secret Origins a few years ago, which is now the current backstory. Either one is fine to start off with, although personally I prefer Emerald Dawn.
Then there's Geoff Johns run, which some have liked, some have hated, but regardless, here is the list of books in the order that they were released in:
Rebirth
No Fear
Revenge of the Green Lanterns
Wanted: Hal Jordan
Sinestro Corps War Vol.1 + 2
Rage of the Red Lanterns
Agent Orange
Blackest Night
Blackest Night: Green Lantern
Green Lantern Corps is also excellent and in a lot of parts better than John's main GL run. The list of books are:
Recharge
To Be A Lantern
The Dark Side of Green
Sinestro Corps Vol 1 + 2 (same as above, collects both Green Lantern and Green Lantern Corps)
Ring Quest
Sins of the Star Sapphires
Emerald Eclipse
Blackest Night: Green Lantern Corps
There are far more books than just this but that should get you off to a good start.
