Shidoh is a Shinigami whose Death Note gets stolen by Ryuk—who then passes it to Light, which eventually lands with Higuchi and later ends up with Mello's gang (specifically with Mello's subordinate Kal Snyder, also known as Jack Neylon).
Shidoh's biggest character trait is his obsession with chocolate. Because he'd been lazy about killing humans and extending his lifespan, he apparently didn't even notice when his Note went missing. Only when his own time was running out did he track down Ryuk, who filled him in: Mello had it. Shidoh then hunts down Snyder in the human world and agrees to team up with Mello's gang against the SPK and Light in exchange for getting his Note back.
After Light reclaims the Death Note from Mello, he returns it to Shidoh just to get him out of the picture and back to the Shinigami realm. In the manga, this whole arc plays out over roughly one volume, but the anime condenses it even further—Shidoh barely appears in episode 28 (just the last few minutes) and episode 29 (which covers most of his Death Note recovery story).
Note on spelling: Death Note: How to Read 13 uses "Shidoh," while the English manga translations and original tankōbon use "Sidoh."
Content compiled by AnimeList.moe from publicly available sources.