I've always wondered how they tracked the Fellowship down and found them on the west side of the Anduin?
Did Saruman maybe know that this was the route the fellowship were most likely to take?
This is discussed by Aragorn in the Departure of Boromir:
It is as Gandalf feared: by some means the traitor Saruman has had news of our journey. It is likely too that he knows of Gandalf's fall. Pursuers from Moria may have escaped the vigilance of Lorien, or they may have avoided that land and come to Isengard by other paths. Orcs travel fast. But Saruman has many ways of learning news. Do you remember the birds?
It's not explicitly stated which, if any, of these was the case, but these are the possibilities given.
This information comes from the synoptic time-scheme that Tolkien made while working on The Lord of the Rings, and was quoted in The Lord of the Rings: A Reader's Companion on pages 360-1 and 378.
January 15: Moria-orcs pursue Co[mpan]y over Silverlode. Driven off by Elves. Messengers leave Moria to Isengard, bringing news of events to Saruman, and also mentioning the appearance of Gollum. (Moria is 260 miles direct to Isengard; but orc-runners cover this in less than 4 days.) Messages also go to Barad-dur, some by evil birds. Barad-dur is about 680 miles from Moria as crow flies, but rumour reaches Sauron in 3 days and Grishnákh and Orcs of Mordor are despatched.
January 18: Orc-runners reach Isengard. Saruman is greatly moved but dare not act independently of Sauron, until he is certain. Sends out scouts under his orc-captain Uglúk. Grishnákh sets out from Mordor.
January 22: Saruman’s scouts return to Moria, and gather a force of mountain-orcs. They cannot penetrate Lorien, but lurk outside especially watching the river-exit.
January 24: Isengarders capture Gollum, and torment him for news. Gollum ... escapes after revealing that Hobbits of Shire were with Gandalf, and enough is said to make Uglúk certain that Ring was with the Company. Uglúk sends news to Isengard of Hobbits; but not of the Ring.
January 26: Grishnákh, having crossed Anduin near rapids, comes up west side, and intercepts Uglúk’s messengers, and learns their news. (He retreats, makes contact with a Nazgûl near Sarn Gebir and awaits orders.)
January 30: Saruman receiving news decides to act on his own. Sends out strong force to join Uglúk, orders them to bring Hobbits alive to Isengard.
February 2: Grishnákh reinforced. Ordered to cooperate with Ugluk (Sauron does not yet suspect Saruman).
February 6: Uglúk scours northern Rohan.
February 10: Uglúk & Grishnákh make contact above Sarn Gebir. Rohirrim drive off Isengarders, who retreat to Emyn Muil, leaving west bank unguarded. Grishnákh watches east bank near Sarn Gebir.
February 22: Grishnákh’s scouts get wind of approach of Coy. A Nazgûl is summoned, but Sauron will not yet permit the Nazgul to cross west of Anduin.
February 23: Orcs are foiled. Legolas shoots down Nazgûl. The Orcs dismayed, but Grishnákh crosses Anduin and daringly pushes down west shore in pursuit. He believes Coy. is making for Minas Tirith.
February 25: Grishnákh and Uglúk meet in western Emyn Muil. They go in search of the Coy.
February 26: After attacking and destroying the Co[mpan]y Orcs hurry towards Isengard. Quarrel bet[ween] Uglúk and Grishnákh (sundown). Grish[nákh] flies north to Sarn Gebir. Ug[lúk] descends into Rohan and begins a wild forced march towards Fangorn with his prey (Merry and Pippin).
Synoptic Time Scheme, Enemies, Jan 15-Feb 26
Most of this does not make it into the main text of the book, except that Aragorn speculates the Moria orcs may have been the ones to tip off Saruman.
He stood for a moment in thought. 'S is for Saruman, I guess,' he said at length. 'There is evil afoot in Isengard, and the West is no longer safe. It is as Gandalf feared: by some means the traitor Saruman has had news of our journey. It is likely too that he knows of Gandalf's fall. Pursuers from Moria may have escaped the vigilance of Lórien, or they may have avoided that land and come to Isengard by other paths. Orcs travel fast. But Saruman has many ways of learning news. Do you remember the birds?'
The Lord of the Rings - Book III, Chapter 1 - "The Departure of Boromir"