The L5R wiki is decent for lore and getting a sense of the characters of the clan. There's a lot of fiction they've (AEG) put out over the years, otherwise if you can get your hands on the RP setting books and things there's a wealth of fluff.
I'd start with familiarizing myself with the families of the Crab: Hida (founding kami and HUGEST of HUGE samurai), the Hiruma (the Hida Champion's bodyguard and supreme salt-lords ever since their castle and lands outside the Kaiu Kabe were taken by the Shadowlands), the Kaiu (boffins, make everything, make the best stuff, build the Wall, maintain the Wall, love the Wall), the Kuni (the Crab's shugenja family and totally fucking metal. Paint their faces, jade strike anything that moves to see if it's tainted, live in a total shithole of horrific tainted mess), the Yasuki (courtiers, merchants, all around pushy, shady, and good to know. Stolen from the Crane clan which...well they weren't going to be friends anyway).
The Crab are associated with most of the southern minor clans, with the Falcon in the Shinomen Mori being the friendliest, but decent relations with the Badger (the death of the Badger Champion in Crane lands a few years back fanned the flames of the now smoldering Lion-Crane conflict), and the Mantis being less hunky dory due to arguments about who daddy loved most from way back when.