The Gemara in Masechet Yoma emphasizes the importance of taking three steps back after completing the Amida, commenting that if one did not do this properly, then it would have been preferable for him not to have prayed at all. In a sense, failing to take three steps back after the Amida almost invalidates the prayer. After stepping back, one recites, "Oseh Shalom Bi’mromav…"
The simple understanding of the requirement to take three steps back is that it displays respect and reverence to G-d. After standing in the Almighty’s presence, we cannot just leave; this would be disrespectful. We instead reverently step backwards, facing Hashem. We step back first with our left foot, showing that we are reluctant to leave, and we do so starting with our weaker foot. The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) offers a different explanation, based on Kabbalistic teaching. When we stand before G-d and recite the Amida, he writes, we are in the realm of "Asilut." And once we finish, we must pass through the realms of "Beri’a" and "Yesira" to return to our world, the realm of "Asiya." We thus take three steps, corresponding to the three stages of our return to this realm.
After one take the three steps back and recites "Oseh Shalom," he remains in place with his feet together until the time for the recitation of "Nakdishach." At that point, one takes three steps forward – starting with his right foot – and keeps his feet together for "Nakdishach." The Kaf Ha’haim (Rav Yaakob Haim Sofer, Baghdad-Jerusalem, 1870-1939) writes that if "Nakdishach" begins immediately after one takes his three steps back, then he should right away take his three steps forward for "Nakdishach," without waiting. If, before "Nakdishach," he needs to step outside, such as to use the restroom, then he does not first take three steps forward. He leaves, and returns to the spot where he was standing, and then takes three steps forward.
If one prays privately, and thus "Nakdishach" is not being recited, then after he takes three steps back and recites "Oseh Shalom," he remains in place for the amount of time needed to walk four Amot – approximately 3-4 seconds – and then takes three steps forward, starting with his right foot. The Gemara strongly condemns one who takes three steps forward immediately, without pausing several seconds, as this shows that his three steps back were not taken out of respect and reverence.
Ideally, before one begins the Amida, he should ensure that he has enough room to take three full steps – toe to heel – backwards after the Amida. However, the Ben Ish Hai writes, if one does not have enough room to take three full steps back, then he takes three smaller steps.
Summary: After one completes the Amida, he takes three steps back, starting with his left foot, recites "Oseh Shalom," and remains in place with his feet together until "Nakdishach," at which point he takes three steps forward, starting with his right foot, for "Nakdishach." If he prays privately, he should wait 3-4 second and then take three steps forward. Ideally, before one begins the Amida, he should ensure that he has enough room to take three full steps – toe to heel – backwards after the Amida. However, if one does not have enough room to take three full steps back, he takes three smaller steps.