You observe, without passing judgment. If a thought comes, just let it come, and don't 'reply' to it. When you notice you drift off, just acknowledge that, without judgment, and continue the process of observation.
For the sake of clarity, let's look at the mind as if it's a separate entity (like a child) that is constantly asking our attention. When we give in, when we reply to our thoughts, its behavior is rewarded and it will keep asking for attention. If you just acknowledge that it's there, but don't act on every thought, the stream will become less and less. The main goal being that it eventually shuts up unless you actually need (ask) your mind to help you with a task.
For the sake of clarity, let's look at the mind as if it's a separate entity (like a child) that is constantly asking our attention. When we give in, when we reply to our thoughts, its behavior is rewarded and it will keep asking for attention. If you just acknowledge that it's there, but don't act on every thought, the stream will become less and less. The main goal being that it eventually shuts up unless you actually need (ask) your mind to help you with a task.