Sit up in your seat... even if you feel your going to fall asleep, don't get up from your seat. If you cannot shake it, then lean forward and rest your arms and upper body on your legs and close your eyes, and gently watch the breath... if you doze off, ok. When you come to, you are already sitting so stretch and yawn and smile, and look around. Then watch the breath again gently.
Now, as to methods of shaking it off -- there are many, but still it can be hard. A big reason you might be dozing off is that you are not making proper use of the eyes. If you close them and allow them to do what they want, then they will start to move around and settle in the same way that they do when you lay down to sleep. And because you are not yet accustomed to meditation, then they body will automatically assume that you are sleeping. So, before you close your eyes you should face an object, sitting about 2-3 feet from it and look at it gently. Take note of the sensation of the eyes and head. Then, without moving your eyes away from the object, close them lightly. Right away you will notice that your eyes move and start doing their thing, and at this point you want to recall to mind how the eyes and head were positioned before.
Second thing is to breath well. Take deep breaths when you feel drowsy, and feel around the body looking for tension or sensations as they come and go. Keep the mind busy with this search. When you find a nice sensation stay with it a little bit and enjoy it, then move on. Go around like this, trying as many ways of analyzing the body and sensations as you can think of. When you notice that your starting to wake up, just allow yourself to feel satisfied in that.
A thing I like to do, is to analysis my posture -- adjusting my arms here, and seeing if that is good. Lean more forward, see if that is pleasing or not. Move my legs a little, see how that feels. Feel around for any tension, then try to relax it.
Give this a read. It is very helpful to remember that 'states' is any thing in the mind or body which is observable. Investigation is any thought (verbal or other) which is trying to understand the details of that state.http://www.accesstoinsight.org/tipitaka ... .wlsh.html
But, monks, when the mind is sluggish, that is the right time to cultivate the enlightenment-factor of investigation-of-states...