There are many ways to meditate. They all seem to lead to the same place, so find one that suits you. The benefits are unique for each person, but both physiological and psychological balance is common. Some of the benefits of meditation will be realized quickly, and others over many months, so don't be discouraged.
Read this important note before you begin.

Keep your spine straight, head balanced on your cervical column. Many people like to pray or do visualization before, after meditating, while still in an altered state. Some teachers of meditation are opposed to this practice while others advocate it. I suggest to do it if it feels right to you.

As a preparation for meditation, bring your attention to the physical act of breathing. Breathe naturally and, with each cyle of the breath, bring your attention to a different part of your body, paying attention to the changes there as a result of the breathing: the rising and falling of the chest; the movement of your belly; the sensation of the air entering and leaving the nostrils; can you feel any movement of your kidney area? How about your pelvis- do you feel your pelvis tilt at all when you breathe? What do you do between breaths? Is there a pause? If you don't feel these things it is okay, just consider them, one at a time, and move on. (This can also serve as a short "centering" meditation that can be done while waiting for a stoplight to change, or as a short work or study break.)

During meditation your business is simple awareness, nothing else. It is a time to connect to your inner Source and let go of the things and roles we get caught up in: work, parenting, concerns and responsibilities. It may be that your meditation is peaceful, or it may be fretful and full of obsessive thoughts. Regardless, daily meditation will have a positive effect on your life.

A mantra is a sound, word, or phrase that is repeated to yourself. It could be spoken aloud, as a chant, or silently, as in meditation. Many people think that the best mantras are sounds which have no clear meaning, and are used as a way of displacing your usual thoughts and moving your awareness inward. There are many mantras ranging from words taken from Hindu Sanskrit to Catholic prayer (especially when "saying the rosary," where the repetition of the prayer is meditative). The correct process of meditation involves a rhythmic internal chanting of a universal mantra or a personal mantra. Talk to a spiritual teacher (acarya) about your personal mantra. It will take many pages, a whole site even, to discuss the science and characteristics of mantra. With a correct incantation of mantra and a constant ideation, our minds will gradually identify with the blissful self within.

Throughout your practice, you should bear the following in mind:
Never force yourself into any position or hold it for longer than feels comfortable. Slow and steady effort brings lasting results.

Always breathe in and out through your nostrils and do not exhale through your mouth. This will give you better breath control and conserve prana or energy. Coordinate your breathing with your mantra.

Sit comfortably. A quiet place is preferred, but not required. Close your eyes. Breathe naturally. Sit for about one minute before you begin thinking the mantra to allow your heart and breathing to calm.

Breathe through your nostrils, allowing the breath to flow in rhythm with your lungs. Feel peaceful and at rest. Consciously relax your whole body. When you practice this for a short while, your consciousness will start to flow gently throughout your body. Imagine a sense of well-being throughout, the prana or the vital force, softly coursing through it.

Gently bring your attention to your breath and begin to think the mantra, gently and easily. Just let it come, don't force it. Allow yourself to be absorbed in it. Allow your thoughts and feelings to come and go with detachment. Don't try to control them in any way. Just note them, and when you realize that you are not repeating the mantra, gently return to the mantra. Do not try to force yourself to think the mantra to the exclusion of all other thoughts.

You may experience a deep state of relaxation but it is okay if you don't. When done, take about a minute to slowly return to normal awareness. Be gentle with yourself when opening your eyes or coming to stand after a meditation.

Practice meditation regularly and enjoy the wonders that it can bring to your life.