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?
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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.