Kataphatic or the Western tradition

I think of this as when I use guided imagery to access my inner knowledge.  I descend down 10 steps to a cave where I have a library of information.  There I can ask any question of myself and receive guidance.  There are also times when I ascend steps to contact a spiritual guide which is beyond myself.  This kind of meditation (I call it hypnosis) I learned at Infinity Institute from my mentor, Anne Spencer.

Apophatic or the Eastern tradition

This is when I sit and allow all my thoughts to settle.  The experience I seek is one of emptiness. I do this to allow my mind to remain as open as possible during the day so that new experiences can be brought to my awareness.  By emptying myself of all thoughts and images I enter a space where I can be totally present in my life.  I am learning this by practicing it 15 minutes a day for a few years now.  I generally meditate with no intent other than achieving a transcendental like state.  (It is not TM that I am aware of.)

However there are many ways to meditate.
Another way that people achieve this meditative ability is by chants.
This is a recording of Tibetan Monks.
There are a series of pictures called the Ten Bulls which can be focused upon in a meditative state.