When you start meditation, first get to a quiet place, like a chair. You can either cross your legs or just sit in the chair. The important thing is to keep your back straight to keep your mind from getting sleepy.
Let your eyes close naturally and stay aware of your breathing, but don't try to control it. Breathe in and out through the nostrils and be aware of how the air feels while it goes in and out of your body.
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First, your mind will probably be filled with random thoughts and it might feel like things are getting more busy. You are actually increasing your self awareness and simply noticing how many thoughts you actually have. Try not to follow your thoughts while they occur. Just try to stay focused on your breathing.
If you notice your mind is wandering, just bring it back. If you can do this for 10-15 minutes, you will get a quiet state of mind. Your thoughts should become clear and lucid, as if it's a calm lake that hasen't been disturbed in a long time. Stay in this state as long as it feels comfortable.
Try to do this breathing meditation each day. You can do it when you first get up or do it before you go to bed. You will usually find the most benefit when you take time out from busy periods. This is a great anxiety-buster: slow, deep breaths helps you combat your body's adrenaline response when stress shows up.