In Mesechta Sofrim, it states that one turns to show the people at one’s right and then to one’s left.
The Acharonim explain that when Mesechta Sofrim states that one first shows the people at one’s right and then to one’s left, it refers to when Hagbah was performed with the writing on the outside. This would be achieved by turning from east to south when Hagbah is performed facing the Aron Kodesh to the east.
However, according to the Ashkenazi custom of having the writing facing the one performing Hagbah, by turning from east to south, one will be showing the writing to those on their left first. This is still done, because one should always turn first to their right.
Some have the custom of turning a full circle. However, based on the wording of Mesechta Sofrim, others have the custom to turn around 180 degrees to one side and after returning to face the front, turn 180 degrees to the other side and return again to face the front.
The turning should be done slowly to allow everyone to see the writing.
It is recorded that the Rebbe once demonstrated Hagbah to the students of the Yeshivah, turning around 180 degrees to the left and afterwards to the right. In contrast to the custom mentioned above, this would be in keeping with showing the writing to those on the right first as per Mesechta Sofrim, based on our custom of having the writing facing the one lifting the Torah.
