The Mechanics

Location
Choose the spot for Your Meditation.  It should be a place where you are unlikely to be disturbed, and where you feel comfortable.  You can have a glass of water beside you, or coffee/tea, but food is not recommended.  Ideally you want to be meditating on an empty stomach.  Plan to eat after you’ve finished.

Posture and Position
If you’re comfortable doing so, you can sit cross-legged on the floor.  If the floor is hard, you can optionally put a soft rug down to create a slightly cushiony spot for yourself, and sit on that.
However it’s not essential that you sit on the floor, especially if you’re a beginner.  A chair is okay too.  What’s the most important is that you are comfortable, and that you get into a position where you’re unlikely to fall asleep.  It’s best not to lie down.  Lying down is for sleep, and bodily rest.  That has its own time and place, and is of course wonderful.  But if the activity you’re focussing on is meditation, you want to be sitting.

Close Your Eyes, and turn your attention inward.
The meditative journey is an inward one, not an outward one.  You have entire outer world, full of distractions, to reckon with for the 23 ½ hours in a day when you’re not meditating.  For your 30 minutes of meditation, you want to block that all out, as much as possible. 

Your attention actually should go inside your body.  Let it wander from your head, down your torso to the belly-button area.  Try to just observe your breathing.  When you inhale ,try to inhale such that it’s your belly that controls the mechanics of that inhalation.  If it feels like the inhalation is being controlled from your nose, mouth or chest, then try to move your attention back to your belly.  You want to use your stomach muscles to push your stomach down and out, so that the air flows in automatically as a result of that.    When you exhale, it’s just a matter of relaxing those same stomach muscles, and the air flows out automatically.

Ideally you want to breathing through your nose, not your mouth.  But this is not a hard rule – if some of the inhalation or exhalation occurs through your mouth, let it be.  But as you concentrate on the mechanics of breathing, the majority should be through the nose.

Try to observe your passing thoughts, rather than forming them.
The idea here is to be an observer of your thoughts.  Ideally you don’t want to be governing those thoughts, with one exception:  If you notice yourself judging another person, then you want to briefly correct that judgmental thought, before returning to the act of observing.

For example let’s say while you’re meditating you see your self thinking that a particular person in your life “deserves” some kind of negative thing to happen to them, or that they have wronged you or someone else.  Your job here is to gently re-think the thought without judgment of that person, so that before that thought dissipates and leaves your attention, you have established to yourself that you are taking a position of nonjudgement.  This doesn’t mean you condone anyone’s bad behaviour.  It’s not about condoning it or condemning it.  It’s about declining to do either.  This can be a difficult position to take for beginners, but it is very important for your own well-being.  You need to understand that the world is going to deal with the bad actors in its own way.  People will get what they deserve, but you should not be a part of that – repayment will be done by the world automatically.  You need to be the impartial observer if you want to find that wealth of inner peace within you.

As the time passes you will begin to feel the effects of your meditation.  You’ll feel like a peacefulness is bubbling up from the belly area, up though your torso and into your mind.  You may get the sensation that this peacefulness is embedded in light.  It might seem joyful, or restful.  You want to be looking for this feeling, and when it comes, try to bask yourself in it.  Let it fill up your mind, and let your consciousness “drink” it until you feel at peace.

This is the act of meditation.  If you can build this habit into a daily routine, the positive feeling described above will increase with time.   You’ll get better and better at finding the feeling, basking in it, and letting it overcome you.  Regular practice, ideally daily, is the way to maximize the benefits.