What is the proper composure for prayer?
The Shulhan Aruch (O.H. 95-1-3) discusses the proper composure that one must have while praying the Amida. One should place both of one’s feet together, bow down one’s head so that one is looking towards and imagine that one is in the Bet Hamikdash with one’s heart directed to the heavens. Furthermore, the Mishna Berura (M.B., O.H 95:5) states that whoever prays without closing one’s eyes does not merit to see Hashem’s Countenance when one passes away. If one must keep one’s eyes open in order to read from a Siddur it is also acceptable. Rabbi Baruch Toledano (Kitzur Shuhan Aruch, § 95), quoting the Zohar, says that one should sway one’s body back and forth while praying and this is based on the verse (Tehillim 35:10) “Kal Atzmotai Tomarna Hashem Mi Kamocha” (lit. “All my bones shall say, ‘Oh Hashem, who is like You?’”) . He cites another opinion (ibid, § 102) that this verse only applies to when one is learning Torah and therefore during the prayer, one should remain still. Both options are viable as long as one is not moving in an exaggerated fashion or one’s eyes are not wandering all about.
Additionally, the Shuhan Aruch (O.H. 96:1) rules that one may hold anything in one’s hands since it may detract from one’s focus. Nevertheless, one may hold a Siddur since it aids in in praying correctly and with proper concentration (ibid:2).
Nowadays, it is possible to access the text of the prayer on one’s smartphone. Nonetheless, this cannot be compared to a Siddur since it has much more potential for distraction and also does not have the inherent holiness of a Siddur. Thus, one should not use a smartphone during the Amida. If one has no other choice, such as if one is traveling and has no access to a Siddur, one should put the phone on airplane mode so as to block the amount of notifications and other distractions. Since a smartphone that is not on airplane mode has a higher risk of distraction, it cannot be compared to a Siddur and therefore one would not be able to recite the Amida from it. During the other parts of the prayer one could use one’s smartphone, but even then, it would be praiseworthy to have it on airplane mode.
Summary: One should maintain proper composure during the Amida. One may not hold anything during the Amida except a Siddur. One may not pray the Amida using a smartphone unless it is on airplane mode.