For most of our lives, the only time we sit perfectly still is when we abandon ourselves to sleep. Because formal sitting meditation practice involves keeping still, the brains of beginning meditators may think it is bedtime and start turning out the lights. Sleepiness is a very common experience for beginners.
There are several remedies for this challenge. The first is to straighten the posture. Sleepiness is usually accompanied by physical wilting of the posture. So straighten up! If that doesn't do it, open your eyes. Letting light in will help wake up your brain. Meditation does not need to be an eyes closed practice. You can open them a little or a lot. Fully open you may find images distracting but slightly open may be enough.
If you are still dozing off, stand up. Keep your eyes open, stand still, and continue practicing. This is also a good way to relieve painful or numb legs.
Over time, sleepiness will be less of a problem.
Often the first thing a beginners notices when they embark on formal sitting meditation practice is a feeling of restlessness. As mentioned above, for most of us, for most of our lives, we never sit truly still. Even when working at a desk, watching tv, or absorbed in a movie, we are fidgeting and shifting. So it is a new experience to sit perfectly still and especially to be still while being aware of our experience as we sit there. The result is often the arising of the habitual pattern of fidgeting. (Yoga practitioners may instead experience a habitual drive to stretch). This restlessness can be quite intense and agitating. The good news is that it is a habit that is usually quick and easy to break. The bad news is that to break it you must sit through it while focusing on it and giving it complete permission to be present. Stated differently, concentrate on the body sensations of restlessness, mapping the locations and other characteristics of the sensations, and letting go of the need to be free from restlessness. Please refer to the section on basics and/or working with discomfort for more detail on this.
It is very common for beginners to struggle with their focus wandering away from its intended object. More advanced meditators also have wandering mind at times, but they don't struggle with it. Beginners assume they should have perfect concentration or they aren't "doing it right". More advanced meditators know that the wandering and returning is just part of the training. Each time your attention wanders and you bring it back, your concentration power gets a little stronger. It is similar to resistance training in athletics - you complete a movement against resistance and your muscles get stronger. So too, you repeatedly bring a drifting attention back to your chosen focus and your concentration gets stronger. The main thing is to let go of any judging thoughts