Earthbending was the most rarely seen bending art during the first few episodes of Avatar: The Last Airbender, but by the end of the sequel series The Legend of Korra, its status as the one of the most fleshed out styles with the greatest number of sub-skills was rock solid.
It's not easy to keep track of so many earthbending forms, so we're breaking down the whole bending style and all the specializations within it.
Basic Earthbending
Understanding the bending art requires an understanding of the basics. Even at the lowest levels Earthbenders are capable of moving pieces of the ground, and ordinarily they become capable of commanding larger pieces of earth the stronger they get. For some benders, like Avatar Kyoshi, the process was reversed -- mastering Earthbending for her involved refining her skill to command smaller objects more precisely.
"Earth" is a loosely defined concept and seems to apply to everything from dirt to stone to coal to crystal. The Earthbending master Toph initially had difficulty with manipulating sand in stark contrast to the Sandbenders living in the Si Wong Desert. Over time she mastered it just like anything else in Earthbending and proved capable of making finely detailed sculptures from sand with just a stamp of her foot.
Seismic Sense
Part of the reason Toph struggled so much with Sandbending initially is because, as a blind person, she relied on Earthbending to "see" her environment. As a young girl she learned the technique from the original Earthbending masters, the badgermoles, and discovered how she could feel the vibrations that passed through the earth to form a kind of sonar image of everything around her. Sand proved to be difficult terrain because its loose shifting nature made the images "fuzzy" to Toph's seismic sense.
Blindness turned out not to be a prerequisite for the ability, as Toph taught the ability to Aang and even passed it on to her children, Lin and Suyin. The ability saved Aang's life during a sneak attack from Ozai in the series' finale, and aided Lin as a detective searching for hidden entrances on more than one occasion. There was an even further application of the ability in lie detection through sensing the subtleties of a person's pulse, and the Red Lotus spy Aiwei embedded himself in the city of Zaofu by offering his talents as a truth seer.
Metalbending
Whereas Toph may have needed the badgermoles to teach her how to use her seismic sense, the invention of Metalbending was all her own. While stranded in a metal container, Toph discovered trace elements of earth within the metal that she manipulated to escape her prison. The Guru Pathik explained during Toph's escape metal was, in truth a part, of the earth from which it was refined, and ever since Toph impressed the lesson upon other Earthbenders that the only thing holding them back from bending metal was themselves.
In Toph's later life, Metalbending was so widespread the city of Zaofu stood as a monument to its success, and an entire police force of metalbenders patrolled Republic City's streets. Platinum proved to be the only metal a Metalbender could not manipulate, but the manipulation of foreign meteorites proved a target did not even need to technically be "earth" for an Earthbender to move it. There were, in actuality, far fewer limits to Earthbending than anyone ever believed.
Lavabending
The rarest sub-skill throughout all of Earthbending is Lavabending, which is demonstrated only by Ghazan and Bolin. While there were Avatars like Roku and his Fire Nation predecessor who showed the ability to manipulate magma, performing a phase change with stone itself was an unheard of ability to Avatar fans until Ghazan made a burning-hot saw blade out of loose rocks to cut himself out of a wooden prison.
The ability proved to be extremely deadly, turning any Earthbenders' attacks against them, as they were reduced to a scalding hot liquid. Bolin's best efforts to learn Metalbending were always futile, and Ghazan never demonstrated that particular ability himself, so although not much is known about the art it could be possible Metalbending and Lavabending are mutually exclusive arts. There has never been a master who controlled both, although history shows it's never a good idea to bet against the limitations of an Earthbender.