Flowing out of Nenuial (Lake Evendim) in northern Eriador, the river flows eastward for about 60 miles before turning generally southward; after about another 120 miles it flows through the easternmost reaches of the Shire, forming its eastern border except for Buckland which lies between it and the Old Forest. Its only major crossings in the Shire are the Brandywine Bridge (or Bridge of Stonebows) and the Bucklebury Ferry.
Skirting the Old Forest to the south, the river then loops south-westward, crossing an old road at Sarn Ford and flowing to the north of the depopulated region of Minhiriath before flowing into the Sundering Sea to the north of the forested region of Eryn Vorn.
The name Baranduin was Sindarin for "golden-brown river". The Hobbits of the Shire originally gave it the punning name Branda-nîn, meaning "border water" in original Hobbitish. This was later punned again as Bralda-hîm meaning "heady ale" (referring to the colour of its water), which Tolkien renders into English as Brandywine.
To the Hobbits of the Shire, the Brandywine was the boundary between the known and unknown, and even those who lived in Buckland on the immediate opposite shore were considered "peculiar".
No tributaries of the Baranduin are described except those near or in the Shire:
Reference
See Brandywine for other uses of the name.