The saying 'Know Thyself' comes to us in the West from Ancient Greece where it was one of the Delphic Maxims. There were originally 147 of these that we know about, though 'know thyself' is easily the most famous (and catchy).
Here are a few other Delphic Maxims: 'Do not make fun of the dead', 'Be (religiously) silent', and 'Make promises to no one'. You can see why the rest of them haven't achieved the popularity of 'know thyself'.
Part of the reason 'Know Thyself' has stayed with us is its truth. Self-knowledge is core knowledge. It's what we need to have any kind of adult life.
So, for those of us who are interested, we should all be asking: "How do you do it and how do you get better at it?"
'Know thyself' is great advice, but it isn't exactly an instruction manual.
The practice of mindfulness, or focused attention training as it is sometimes called, comes to us from the East. It derives from Buddhist meditation practices. Though, as it appears today in corporate and educational settings, it is devoid of outward religious ceremony or trappings.
This Eastern-based practice provides you with essential tools to pay attention to thoughts and to be aware of the interactions between mind and body. Mindfulness is paying attention to you mind. By paying attention to your mind and body - deliberately, intentionally, for at least a little while - you begin to develop a greater awareness of what's going on.
In this way it is a tool for real, intentional self-awareness and proactive living.
If we consider it in this way it can be seen as a great example of the melting pot of our modern global culture. East is meeting West (as it often does) and one is the mirror of the other. Mindfulness practice can become a tool to achieve that core Western goal of 'know thyself'.
The path is winding but the view is nice.