Shelob resides in the appropriately named Cirith Ungol (Spider Pass), a series of caves that lead into Mordor. (You can just walk into Mordor, if by "walk" you mean "be chased by a giant man-eating monster.") The caves are full of her webbing, some of which is as strong and thick as rope. Sauron tolerates her presence as a convenient guardian of this route, despite her consumption of the occasional Orc patrol. Unlike her ancestor, Shelob hungers for flesh rather than light.
Gollum was strangely reverent of her, and she allowed him to pass safely through Cirith Ungol—maybe because of the Orcs that sometimes followed him in, or maybe simply because Gollum is skin and bones. Either way, Gollum tricked Frodo Baggins and Samwise Gamgee into the caves in a bid to get the One Ring back.
Shelob's venom can paralyze her prey, rather than kill outright, allowing her to store them for fresh consumption later. After paralyzing Frodo, Shelob tries to kill Sam, but Sam manages to stab her underside with Sting. Shelob retreats back into the darkness, her fate unknown.
In the movies, Shelob appears during The Return of the King, rather than at the end of The Two Towers. Additionally, she has a stinger on the end of her abdomen, and stings Frodo in the torso, rather than biting him in the neck.
In Fan Fiction
Shelob tends to remain in character in fan fiction, since even a bad writer would be hard pressed to get "big hungry carnivore" wrong. Of course, spiders aren't pretty, so Shelob is sometimes left out of retellings of the journey to Mount Doom entirely. Be on the lookout for Warrior Sues who best the beast far too easily; after all, Shelob is in her natural element, surrounded by her webs, and was only thwarted by Sam when she tried to physically crush him, heedless of his sword.