I fairly commonly get asked about the problem of getting very sleepy while meditating.
Here are some fixes to try:
1) Always meditate with your eyes open (in a relaxed position, slightly downcast, maintaining a soft focus on an area of the floor a few feet in front of you). This is the traditional meditation technique used in Zen.
2) If you start feeling groggy, open your eyes wide and make the "Lion pose" shown below. Literally roar two or three times. Read more about it here.
2) Silently count your breaths, at least at the beginning of each meditation session (until you become practiced at meditating without falling asleep). Silently note "One" on the in-breath; "Two" on the out-breath. Over and over and over...
3) Meditate at the point of the day when you feel most awake. For some, this is early morning; for others, noon; for night-owls, midnight might be the most awake period.
4) Don't meditate more than 10 minutes at a time in the beginning. Try this twice a day. Gradually increase to 20 minutes, twice a day. No need to go beyond 20 minutes per session, unless it really just "feels" right (but even so, don't meditate more than an hour per session X 2).
5) I suppose I'll mention the obvious: Be sure to get enough sleep at night!
6) If none of the above work, try walking meditation. (Actually, try walking meditation in any case; it's quite enjoyable.)
Remember that meditation is not a panacea! The chief benefit of meditation is that it allows consciousness to dis-identify with sensations, feelings, and thoughts. All these continue to arise, of course, but one becomes aware of the fact that they do not bind (they come up, they flux for a bit, and they vanish). In other words, meditation is the practice of non-reaction: remaining open like the sky while phenomena come and go, come and go. If you'll kindly agree with yourself not to fight (or chase) all the stuff that endlessly comes and goes while meditating, you will find that eventually the mind slooooows down and becomes more and more subtle, until you are able to enjoy gaps of silence and stillness in which nothing at all arises. Then you recognize that you are a vast clarity, an immaculate luminous space, a pure (object-less) Capacity. Or, as they say in Zen, "You are the Host; everything takes place in your own house."