One reciting the Amida must bow her head slightly, so that her eyes point humbly downwards; she must imagine herself standing in the Temple and direct her heart toward heaven (Yevamot 105b; SA 95:2).
The kabbalists praise one who prays with her eyes closed. However, even one who looks into her siddur follows the law le-khatĥila. Many Aĥaronim recommend praying from a siddur, so that one can have more kavana in her prayer (MB 95:5; Kaf Ha-ĥayim 9-10; and see BHL, quoting Ma’amar Mordechai).
Regarding one’s hands, Rambam writes (MT, Laws of Prayer 5:4) that one should place her hands on her heart while interlocked, right over left, so that she stands as a slave before her master, in awe and fear. This is also the opinion of SA 95:3 and Kavanot Ha-Ari (Kaf Ha-ĥayim 95:12). Many maintain that the placement of the hands depends on local custom; where Rambam lived, it was indeed customary to stand before kings and ministers in the manner he described. However, people in other areas practiced differently. For instance, in Christian lands people customarily stood with their arms folded, while in Islamic land they would stand with their hands behind their backs, symbolically indicating that they do not even have their hands without the consent of the One Who they face in prayer (Mahari Aboab, cited by Beit Yosef; MB 95:6). Nowadays, according to this, in addition to what Rambam wrote, it is also permissible to stand with one’s hands adjacent to her body or holding a siddur, or resting on a table next to her siddur, for that, too, is considered standing respectfully. However, one should not stand with her hands in her pockets or on her hips, for it is inappropriate to stand that way in front of respected people.
Many people are accustomed to “shuckling” (swaying) while reciting the Amida. Rema writes (§48; MB 95:7) that this is the proper way to practice le-khatĥila, as it expresses the excitement and trepidation of the prayer experience, and in order to involve one’s whole body in the service of prayer, as the verse states: “All my bones will say: ‘God, who is like You?’” (Tehilim 35:10). In contrast, Shlah states that one should not sway during prayer. On the contrary, standing motionless strengthens one’s kavana. Furthermore, it says it is not respectful to sway. If one were to come before a human king and begin to shake his whole body, the king would dismiss him immediately. If so, one should certainly not act that way in prayer. Shlah explains that the recommendation to sway applies specifically to Torah study or to singing songs and praise. However, during the intense and inward-focused Amida, in which we stand before the King, it is not proper to move at all; only one’s lips may move (Shlah, Masekhet Tamid, Ner Mitzva). Since each custom has opinions on which to rely, every person may practice in the manner that allows her to concentrate the best (MA, MB 48:5; and see Kaf Ha-ĥayim 48:7-9).