The Gemara in Masechet Yoma, Daf 39A, discusses the procedure for the Yom Kippur service in the Bet Ha'mikdash, and mentions that as the Kohen Gadol stood in the Azara (courtyard) of the Temple, the Segan, or Kohen Gadol's assistant, would stand to his right. Another Kohen, called the "Rosh Beit Av," would stand to the Kohen Gadol's left. The Gemara derives from this arrangement a general rule concerning the proper protocol when two people escort a person of distinction. Namely, the individual considered second in importance to the prominent individual should stand to his right, while the one deemed third in importance should stand to the left. This Halacha is codified in the Shulchan Aruch (Yoreh Dei'a 242:17).
Interestingly enough, the Sages teach that this arrangement is observed by the angels, as well. When the three angels visited Avraham after his circumcision, Michael, the most prominent of the three, stood in the middle, with Gavriel – who is second in importance to Michael – to his right, and Refael to his left.
The Halacha concludes that when a Rabbi walks with two other people, the other two should walk a step behind the Rabbi, as an expression of respect. They should not walk directly beside him, and should certainly not walk ahead of him, which would be an expression of arrogance and impudence. The work "Chashukei Chemed" addresses the situation where a Rabbi and his students drive together in different cars to a certain destination, and the students wish to move ahead of the Rabbi's car to circumvent the traffic in their lane. The "Chashukei Chemed" rules that doing so would be forbidden because of the Halacha established by the Gemara, forbidding one from walking ahead of his Rabbi.
Summary: When two people escort a Torah scholar, the person second in importance should walk to the Rabbi's right, and the other individual should walk to his left. Students walking with their Rabbi must remain a step behind him as a sign of respect, and certainly should not walk ahead of him. Likewise, a student should not cut in front of his Rabbi while driving if they set out together.
