Hi, ShadowInTheWind ~
I can't tell the differences between the normal meditation and mindfulness meditation since I only practice mindfulness meditation
What is want to be achieved from mindfulness meditation is to be aware of your stream of thoughts, or even sensations on and/or within your body but not to react to them. There are certain principles that we have to practice throughout the meditation which are non-judgmental, non-striving, acceptance, focus, continuous effort, and so on.
Within the Buddhist tradition, it is also known as Vipassana meditation. One of the widely spread school of meditation is the Vipassana meditation as taught by S.N. Goenka. You may visit their website at http://www.dhamma.org/
Another kind of popular mindfulness meditation is what has been taught by Dr. Jon Kabat-Zinn through his Mindfulness-Based-Stress-Reduction program (MBSR) Clinics which are highly available in the U.S.A. You may read his book such as the Full Catastrophe Living. In that book, he describes in-depth about the step-by-step for the mindfulness meditation. There are also many speeches of him that you can access from youtube.com, such as this one http://www.youtube.com/watch?v=3nwwKbM_vJc
"God, grant that I may seek to comfort rather than to be comforted; to understand,rather than to be understood; to love,rather than to be loved." - Alex Wolf