This, is the essence of Zazen, the Zen sit. To sit still, and observe your thoughts and feelings with detachment; as if they belonged to someone else. As if they are the background noise of a radio playing, a TV show you are not very interested in. Just allow them to surface and pass through you, without reaction, without attachment, without movement. Eventually, the noise fades, and there is silence.
The mind of a Zen master, is silent. He acts, in perfection, without thought.
This sort of detached observation is the simplest, and yet the most difficult type of meditation. It sounds simple enough, but in practice it is hard to simply let your thoughts go by without engaging the dialog in your head and becoming emotionally involved in it.
It gets a little easier, if you attain the Witness state. Instructions for attaining the witness state, are in the Chakras section.
Instead of sitting still, try it in combination with the walking meditation.