The Gemara in Masechet Shabbat (10) tells that the Sage Rava would "fold his hands" while praying the Amida, like a servant pleading before His master. He would place one hand in the other over his heart and stand before God in prayer like a servant humbly beseeching his master.
Accordingly, the Shulhan Aruch (Orah Haim 95:3; listen to audio recording for precise citation) rules that while reciting the Amida, one should place his right hand over his left hand, and place them over his heart. He adds that one should stand in a manner that reflects fear, awe and trepidation. The Shulchan Aruch further notes that it is improper to place one's hands on his hips as he prays the Amida, as this posture would be an expression of arrogance.
Rav Moshe Cordovero (Spain-Israel, 1522-1570) maintained that while reciting the Amida one should place his right hand over his left hand (as the Shulhan Aruch rules) and insert his thumbs into his hands such that they are not exposed. The right thumb should be inserted into the left hand, and the left thumb into the right hand, in order that the thumbs cannot be seen.
It should be noted that this requirement to fold one's hands together during the Amida applies only if one recites the Amida without holding a Siddur. If a person holds a Siddur as he prays the Amida, then he may certainly use his hands to hold the Siddur, rather than place them over his heart.
Summary: One who prays the Amida without holding a Siddur should place his hands over his heart, with his right hand covering his left hand and the thumbs inserted into the hands such that they are concealed. It is improper to recite the Amida with one's hands on his hips.
