"To sit in zazen meditation is not a method to
 find the right state of mind. 
 To sit in zazen, is itself to have the right state of mind. 
 There is no need to obtain some special state of mind."

How to sit in Zazen meditation.

Find a peaceful spot. Sit facing the wall.

The traditional way of sitting is in a full lotus posture. This is how most monks sit. But you can sit the way you want, as long as you can keep your back straight without straining it. If you sit in a chair your back should not be leaning against the back support. 
I find that if I sit down as far back as I can on the seat, so that my butt touches the back support, my back will keep straight and not touch the support. 
Your neck should also be straight. Don't bend it. Imagine that there is a string attached on the back of your head and it's lifting the back of your head up. When you feel a little stretch in your neck, move your chin in towards your chest a little.
In zazen your eyes are slightly open and resting on a spot about one to two meters in front of you, on about a 45 degree angle. 
Place your hands in your lap. And place your left hand in your right with palms facing up. Then let the tips of your thumbs touch. Like this.
 
  

When you have the right posture, concentrate on your breathing. Just breathe normal through your nose. Listen to and feel your breath going in and out, like the waves on a beach. Do not try to empty your mind. That is impossible. Let thoughts come, but do not serve them tea. Let them sail through while you go back to your breath. 

Always go back to your breath. Your breath is your safe place. It is always there.
 
Let sounds be sounds, smells be smells, tastes be tastes and thoughts be thoughts.
 
Back to your breath. 

Do not sit in search of enlightenment. 

To sit zazen is enlightenment.  

It is best not to sit for longer than 45 minutes at the time. 
You can sit for example 20 minutes, stand up in silence and walk around in silence (kinhin) for 5-10 minutes maintaining the connection to your breath. 
Then if you want, you can sit down again and continue your zazen. 
If you sit for to long, you will become tired and might fall asleep. 
Zazen is hard work, so to keep your energy up, you should stand up and wake your body. You can even get a cup of tea or coffee to wake yourself for the next round of zazen. 
When you are done sitting, don't leave your practice on the pillow or chair. 

I have found that after I started practicing zazen, my anxieties are not gone, but I can control them much easier. I see that they are the product of the mind. Real but not reality. 

Good Luck!