Anduin is the Sindarin name for the Great River of Wilderland, the longest river in the Third Age (the original Sindarin name means Long River). It flowed from its source in the Grey and Misty Mountains to the Mouths of Anduin (Ethir Anduin) in the Great Sea (Belegaer). In her Atlas of Middle-earth, Karen Wynn Fonstad estimates a total length of 1,388 miles.
The Anduin began as two different streams near where the Misty Mountains met the Grey. These were called the Langwell and the Greylin by the Éothéod when they lived in the triangle of land formed by it. Their old capital Framsburg was built at the confluence of these streams where the Anduin proper began. The Langwell had its source in the Misty Mountains, close to Mount Gundabad, and the Greylin began in the westernmost heights of the Grey Mountains.
The Anduin flowed parallel to the Misty Mountains in a broad vale which formed the western part of Rhovanion, lying between the mountains and Mirkwood. After passing Lorien, the river and mountains parted company, and the river flowed through the Brown Lands (which may have been home to the Ent-wives) via the North and South Undeeps until it flowed past the Emyn Muil and Argonath and entered a lake (Nen Hithoel) through Sarn Gebir (a series of ferocious rapids). Thence it flowed over the Falls of Rauros, and past the Mouths of Entwash and the marshes known as the Wetwang (Nindalf). It then passed between the White Mountains and the Mountains of Shadow by the capital of Gondor, Osgiliath, before swinging past the harbour of Harlond close to the Rammas Echor south of Minas Tirith (Barbara Strachey, in Journeys of Frodo, places the harbour just outside the wall), and the Emyn Arnen and down past the port of Pelagir, entering the Great Sea in the Bay of Belfalas in a broad delta known as the Mouths of Anduin.
In order from north to south: the Rhimdath (Rushdown), the Ninglor (Gladden) which joined at the marshes known as the Gladden Fields, the Celebrant (Silverlode), the River Limlight, the Onodló (Entwash), the Morgulduin, the Erui, the Sirith and the Poros. The first five had their sources in the Misty Mountains, the Morgulduin and (presumably) the Poros in the Ephel Dúath on the border of Mordor, and the rest in the White Mountains.
There was a bridge in the city of Osgiliath, broken by the forces of Mordor.
During the March of the Elves in the Time of the Trees, the Nandor left the Eldarin host when faced with the great heights of the Misty Mountains, and lived in the Vale of Anduin. Some of those people later left and became the Green-elves of Ossiriand, but Elves remained present even until the time of the War the Ring, strengthed by refugees from Beleriand (at the end of the First Age) and Eregion (during the Second).
Settlements in the Vale of Anduin during the Third Age included the northman city of Framsburg, Beorn's Halls and the Stoor settlements near the Gladden Fields (where Sméagol/Gollum) was born. It was in the Gladden Fields in the northern reaches of Anduin that Isildur was slain and the One Ring lost; and it was there, more than two millennia later, that Déagol found the Ring and Sméagol took it from him. Rhosgobel, home of Radagast the Brown, and the Elven Realm of Lothlorien also lay in the Vale of Anduin.
Once it had entered Gondor the river flowed past Osgiliath and Minas Tirith and then Pelagir, close to the sea. After the fall of Osgiliath the river effectively marks the eastern limit of Gondor's influence.
The principal islands appear to have been Cair Andros, on the borders of Ithilien and Tol Brandir in Nen Hithoel. Carrock, in the north was where the Eagles deposited Thorin and Company. There was also an eyot, where the Fellowship rested during their travel between Lorien and Parth Galen.