While davening Shemona Esrei, one’s hands should be in the same position they would be in were the person speaking to a human king, dignitary or president. (During Shemona Esrei we are standing “L’fnei HaMelech- in the presence of the King [of Kings]!”)
A person’s hands may not be in their pockets, crossed over their chest, or any other disrespectful position during Shemona Esrei (and ideally not at any other part of davening either)
The correct position is dependent on each place and time.
In the old days the right hand was placed on top of the left hand when in the presence of a king.
Today it is acceptable for the hands to be placed gently at one’s side, although some people still have the custom to place the right hand on top of the left hand and hold it near the heart, as there are kabalistic reasons for standing in this position. (See Shulchan Aruch Siman 95:3 and Mishna Berura S”K 6. See also Shulchan Aruch HaRav Siman 95:4. This is a proper custom which many Yirei Shomayim, G-d fearing Jews, follow.)
For Kabalistic reasons, the left hand should never be placed over the right hand as the power of the right (Rachamim) should always overpower the left (which is symbolic of the Yetzer Hara). (See Darchei Moshe Siman 95:3)
Thus, left handed people who place their hands near their heart while davening Shemona Esrei, should also make sure to have their right hand on top of their left hand.
All of the above applies to women as well as to men.
If while davening Shemona Esrei, one finds his/her mind wandering, he/she should stop until the foreign thoughts pass and then resume the davening with concentration.
In order to get the mind back to the task at hand (i.e. talking to Hashem), one should focus on thoughts that humble the heart and bring it to center on serving Hashem… (See Shulchan Aruch Siman 98:1)
A Segulah (spiritual remedy) for clearing the mind before starting to daven is to pass the right hand three times over the forehead, and each time say the Posuk (Tehillim 51:12, in the chapter of Teshuva) “Lev Tahor Bra Li Elokim, V’Ruach Nachon Chadesh B’Kirbi, Create me a clean heart, Hashem; and renew a steadfast spirit within me.”.
Likewise, if an unclean or otherwise foreign thought enters the mind during Shemona Esrei (or any other part of davening where talking out is prohibited), the right hand should be passed over the forehead three times and the abovementioned Posuk “thought” in the mind with each passing of the hand. (as actually saying it then would be a Hefsek). (Mishna Berura Siman 98:2 quoting the Elya Rabbah in the name of the Shl”a HaKadosh)
Being as this is a Segulah based on kabalistic sources and ideas (right hand representing Rachamim etc.) it applies equally to lefties and righties. (Shu”t Be’er Moshe Vol. 2 Siman 3:7b)
This d’var halacha comes courtesy of HalachaForToday.com