The geography of southern Gondor to the west of Minas Tirith was characterised by a series of rivers rising among the White Mountains and flowing generally southwards into the wide Bay of Belfalas. Sirith was important among these; after the short lesser river Erui, it was the first major river westward of Minas Tirith.
Like the other rivers in this part of Gondor, Sirith had its springs among the southern slopes of the White Mountains, and from there it flowed southward through Lebennin. On its upper course, it was joined from the west1 by Celos, another stream out of the mountains, and then ran on almost directly southwards.
The river Sirith did not empty directly into the Bay of Belfalas, but instead into the wide channel of Anduin as that Great River approached its own Mouths. At the outflow of Sirith, the Dúnedain had built Pelargir, which had an important port city long before even the founding of Gondor. At Pelargir Sirith was crossed2 by a road approaching from Linhir to the west before running on northward and eastward towards Minas Tirith.
Notes
1
A map originally redrawn for Unfinished Tales shows Celos flowing into Sirith from the east, not the west. Christopher Tolkien points out his own error in The History of Middle-earth volume VII, and later editions of the map generally amend the labelling of the rivers.
2
There were two important river-crossings at Pelargir: one across the mouths of Sirith, and another across the (very considerable) width of Anduin, leading towards the Harad Road. We're not told specifically whether these crossings were bridges or fords, but the former seems the more likely option. Given that Pelargir was founded by Númenóreans at the height of their power, it seems difficult to imagine that they would not have constructed bridges to their most important port city.