The answer to this question depends on which interaction you mean. But either way, the wikipedia article on Argonaute is a surprisingly good starting point.
If you mean, how does an Argonaute protein complex consisting of proteins and small RNAs (miRNAs, siRNAs, piRNAs) bind a target to effect gene silencing?:
Argonaute proteins bind different classes of small non-coding RNAs, including microRNAs (miRNAs), small interfering RNAs (siRNAs) and Piwi-interacting RNAs (piRNAs). Small RNAs guide Argonaute proteins to their specific targets through sequence complementarity, which typically leads to silencing of the target. Some of the Argonaute proteins have endonuclease activity directed against messenger RNA (mRNA) strands that display extensive complementarity to their bound small RNA, and this is known as Slicer activity.
If on the other hand, you mean how do Argonaute proteins themselves form a complex with small non-coding RNAs?:
The structural basis for binding of RNA to the Argonaute protein has been examined by X-ray crystallography of the binding domain of an RNA-bound argonaute protein. The phosphorylated 5' end of the RNA strand enters a conserved basic surface pocket and makes contacts through a divalent cation such as magnesium and by aromatic stacking between the 5' nucleotide in the siRNA and a conserved tyrosine residue.
Some handy resources: