I assume you haven't been given this assignment "cold turkey", without suitable in-class learning of related technical matters.. right?
The air interface for GSM is called "Um", and is shared with GPRS, which is what GSM 2.5 is known as. SMS is transmitted one of two ways to a mobile station (MS), depending upon whether the MS is on a voice call or not at the time.
For an idle MS, the SMS info is carried over the SDCCH; for one on a call it is sent over the SACCH logical channel.
I found
this link which may help (or not). It takes a rapid tour through the layer-2 frame structuring, which sits on top of Um.
I wonder how detailed or not they want the answer to be..