I heard 2 ideas
1. When coming go the shortest way, when leaving go the longest way.
2. Always turn right
So what needs to be done?
Sources for both ideas, and what to do, please.
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(Almost all the references in this answer were added thanks to @hazoriz. I am grateful to him)
When one get Sefer out from the Aron, if the Aron is on the East side, and the Bima on the West side, one would skirt round the northern side which is his right side. When one get back the ST to the Aron, one would skirt round the Southern side which is his right side. But The Magen Avraham (141, sk 7) said that to get out the ST and for reading one needs to take a short way.* But the Peri Megadim (Eshel Avraham, sk 7 in name of the Levush disagree with the comparison between the man who was called to read and the Chazan with the Sefer Torah, who need always turn right). Rabbi Israel Meir Kagan in Mishna Berura sk 25 and Shaar Hatsiun sk 30 ruled as the Peri Megadim.
Shorter length ways are mentioned for this for the man who is called to read Torah. It is in siman 141, 7. To come rapidly makes honor to the congregation and to the Tora, to get away by a length way would demonstrate that the man is freed from a burden.
*The MA reports a Bet Yosef in siman 128.I found the issue of Est --> North --> West |-->South --> Est for the ST, See Machatsit Hashekel sk 7, who ask that lechaora, the Bet Yosef is not a proof for the opinion of the Magen Avraham.