The three steps taken before Shemoneh Esrei:
Three steps forward: Some Poskim rule that when one stands to Daven [Shemoneh Esrei] he is to go forward three steps, like one who advances forward towards something that he needs to do. Practically, it is proper to suspect for their opinion [and so is the custom of all Israel]. [It is likewise customary to take three steps backwards prior to taking three steps forward, as explained in the Q&A.]
Summary [includes Q&A]:
Prior to beginning Shemoneh Esrei, one is to take three steps backwards, and then three steps forwards, beginning with the right foot each time. This is to be done directly after Goal Yisrael, although some take three steps back upon saying the words Tehilos Lakeil Elyon.
Taking three steps backward:
Some Poskim rule that one is to take three steps backwards prior to taking three steps forward before Shemoneh Esrei. Practically, so is the custom. [Although this custom is not recorded in the earlier Poskim, or the Shulchan Aruch, nonetheless, it carries all the weight of a Jewish custom, and contains both Halachic and esoteric meaning.]
When is one to take the three steps in Shacharis?
The three steps forward is taken after Goal Yisrael even by Shacharis. However, some Poskim rule that by Shacharis, the three steps backwards is to be taken as soon as one stands up by the words of Tehilos Lakeil Elyon, and one then takes three steps forward after Goal Yisrael. Many, however, are accustomed to take both three steps backwards and forwards only after Goal Yisrael, and so was witnessed to be the Rebbe’s custom.
With which foot is one to take the three steps back and forward?
One is to do so with his right foot. [However, one who is left footed, is to use his left foot.]
Is one to take three steps back if someone in back of him already began Shemoneh Esrei?
If the person in back of him already began Shemoneh Esrei, then one is not to take three steps backwards if he is within one’s four Amos.
 Admur 95:2; Rama 95:1; Rishonim in next footnote; Elya Raba 95:3; Kitzur Shelah Dinei Tefilas Yud Ches; Chut Hashani; Siddur Yaavetz 19; Chesed Lealafim 93:6; Kaf Hachaim [Falagai] 15:2; Kitzur SHU”A 18:2; Ben Ish Chaiy Beshalach 3; Aruch Hashulchan 95:3; Kaf Hachaim 95:6; Piskeiy Teshuvos 95:2; Omitted from Levush 95
The law if one went to Shul versus at home: Some Poskim suggest that one is only required to take three steps forward before Shemoneh Esrei if he did not walk to Shul, or any other place to Daven. If, however, he already walked somewhere for the sake of Davening, then he has fulfilled the necessity of three steps and does not need to repeat it. [Elya Raba ibid in explanation of omission of Levush 95; Nachalas Tzevi 95, brought in P”M 95 A”A 1 and Kaf Hachaim ibid] Practically, however, one is to take three steps forward in all cases, as it is not a big deal to do so. [P”M ibid; Kaf Hachaim ibid; Aruch Hashulchan ibid that the custom is not so] This especially applies according to the additional reasons brought behind this custom.
Other opinions: Some Poskim imply that there is no need to take three steps [backwards or] forwards prior to Shemoneh Esrei. [Omitted in Levush 95; Custom of Munkatzher, as brought in Darkei Chaim Veshalom 154 not to take three steps at all; Custom of Steipler as brought in Orchos Rabbeinu 1:59]
 Rokeiach 322; Machzor Vitri 21; Siddur Rashi
 The reason for three steps: 1) This corresponds to the three times scripture states the word Vayigash in regards to prayer; one time by Avraham “Vayigash Avraham”, one time by Yehuda “Vayigash Yehuda”, and one time by Eliyahu “Vayigash Eliyahu”. [Darkei Moshe 95 in name of Rokeiach ibid; Ateres Zekeinim 95; Biur Hagr”a 95; Kneses Hagedola 95:1; Elya Raba 95:3; Yifei laleiv 95:3; Kaf Hachaim 95:6] 2) Alternatively, the reason is because the verse states Ragleihem Regel Yeshara, and the word Ragleihem is two steps, while Regel is one step, for a total of three. [Elya Raba ibid] 3) Alternatively, the reason is because it corresponds to the three steps that Moshe took forward, towards the cloud, of Choshech, Anan, and Arafael. [Kitzur Shelah Dinei Tefilas Yud Ches, brought in Shalmei Tzibur p. 199 and Kaf Hachaim ibid] 4) Alternatively, the reason is because it corresponds to the three steps that the Jewish people took towards Mount Sinai after being distanced by the sound. One who does not do so makes it appear as if the Jewish people were not brought closer to G-d, and reaccepted, after they were distanced from Har Sinai Chas Veshalom. [Chut Hashani 54, brought in Shalmei Tzibur and Kaf Hachaim ibid]
 Admur ibid; All Achronim ibid
 Kitzur Shelah Dinei Tefilas Yud Ches in interpretation of Rokeiach ibid [brought in Kaf Hachaim ibid]; Chut Hashani 54 that just like it is an obligation to take three steps backwards, so too he must take three steps forward; Siddur Yaavetz 19; Chesed Lealafim 93:6; Kaf Hachaim [Falagai] 15:2; Kitzur SHU”A 18:2; Ben Ish Chaiy Beshalach 3; Kaf Hachaim 95:6; Piskeiy Teshuvos 95:2
Other opinions: Some Poskim rule that one is not required to take three steps back if he is by the wall and the like. [Elya Raba 95:3; M”B 95:3 in name of Elya Raba ibid, although he makes no mention of the last words of the Elya Raba that this only applies if one is standing by a wall. The M”B plainly quotes him to rule that one does not need to take three steps back at all. Vetzaruch Iyun as to the intent of the Elya Raba in this stipulation.]
 M”B 95:3 in name of Magen Giborim
 The reasons: 1) It is done as in order to take three steps forward one must first take three steps backwards. [Kitzur Shelah ibid; See Elya Raba ibid] 2) It is done to represent the three Milin that the Jewish people were distanced from Har Sinai, and then came close. [Chut Hashani ibid] 3) It is done based on Kabalistic reasons. [Ben Ish Chaiy ibid] 4) It shows that one is fearful of G-d, and hence distances himself before coming close. [Kaf Hachaim ibid; Piskeiy Teshuvos 95 footnote 14]
 Tehila Ledavid 111:1; See also Admur 111:1 regarding Adniy Sefasaiy Tiftach
The reason it is not an interval: As the steps are done in preparation, and for the need of Shemoneh Esrei. [Tehila Ledavid ibid]
 Kitzur SHU”A 18:2
 The reason: This is done in order to diminish in a Hefsek between Goal Yisrael and Shemoneh Esrei.
 See Tehila Ledavid ibid from whom we can imply that just as the three steps forward may be taken after Goal Yisrael, and is not considered a Hefsek, so too with the three steps backwards; See Piskeiy Teshuvos ibid
 See Maharil in name of Orchos Chaim, brought in Beis Yosef 123, based on Yuma 55b that all turns should be done to the right; See Admur 123:5 and M”A 123:10 for the reasons for why after Shemoneh Esrei we step back with our left foot. Now, theses reasons imply that before Shemoneh Esrei one is to specifically move his right foot first; Piskeiy Teshuvos 95:2 in name of Orech Neman 95:3
 See Admur 123:5; Tzemach Tzedek Orach Chaim 4:6 and 5:8 regarding Netilas Yadayim, and based on Admur 183:7 that a lefty is to hold the Kos Shel Bracha in his left hand; 651:14 that a lefty is to hold the Lulav in his left hand
 See Admur 102:4-5 and Michaber 102:4 that it is forbidden to walk in front of the Davener, within four Amos; Elya Raba 95:3 who writes that seemingly one is not require to take three steps back if he is by the wall and the like, and one who is Davening Shemoneh Esrei, of which it is forbidden to take three steps back, is no different; See Shevet Hakehasi 2:49; Halichos Shlomo 8:33 in name of Rav SZ”A; Piskeiy Teshuvos 95:2 footnote 17