Observing Thoughts and Emotions in Meditation

Be aware of them, so that you are able to directly perceive that you are not your thoughts/emotions, but the consciousness, which is a silent observer. This way you train to avoid identification with them, which will stop feeding energy to the thoughts/emotions. And when they get no energy, they cannot sustain and thus vanish by themselves.
If you find a thought or emotion, that you want to study more (i.e. because your intuition is tingling, because it is especially hard to disengage your consciousness from it, etc), then you hold it in your imagination.