Read pages 1-5 of the Basic Method of Meditation, which are the official instructions for the course.
There's a lot more space on this meditation. Follow Ajahn Brahm's guidance, then use the feedback from what you're experiencing to judge when to move between the 3 stages. When moving to the breath, start by doing at least 5 cycles of breath counting. If you're not losing count, you can try following the breath without counting.
Sleepiness is a common challenge for meditators. If you're falling asleep it's a sign that your posture is relaxed (good), but not quite alert enough. You can counter this, and make it part of the meditation, by straightening your spine each time you notice yourself "sinking". Think of it as the physical counterpart of noticing your mind wandering, and bringing it back to the breath.
There's been so much coverage of mindfulness in recent years, I thought I'd share Ajahn Brahm's concise clarifications on what mindfulness is, and why it's worth cultivating.
You've already been practising mindfulness of the body (at the start of your meditations when you settle in), mindfulness of thinking (noticing and letting go of thoughts about the past and future), and mindfulness of the breath. Mindfulness meditation means applying mindfulness for a sustained period. The breath is often used as a meditation object of meditation, because it's something you always have with you, which is emotionally neutral, and constantly changing.
If there's one video you watch, which reminds you how to meditate, it's Ajahn Brahm's simile of the cup (YouTube, 3m 45s).
Ajahn Brahm describing the Peace-o-meter (YouTube, 3m), a simple but powerful way to use mindfulness as a feedback mechanism to increase peace, and happiness.