Most fireplace screens are made with mesh, as the Grand Metal Fireplace screen, found on our greatfiresides.com website..  The mesh allows the flame to be seen and the warmth to be felt, while it also helps protect your home from ashes and fly away embers.

Your screen is very easy to clean.
1.  Take a damp cloth and gently wipe it down.
(You may want to wipe off the excess soot, before you touch it with a damp
cloth.  Make sure your screen is not too hot to touch)
2.  Rinse your cloth in some warm soapy water and wipe it down a second time.
3.  After you have got most of the soot off, wipe it down one last time with a damp
non-soapy cloth and let it air dry or use a dry towel to dry it off.

If it is easier for you, you can take the screen to your sink and spray it down with a sink hose, add a touch of dish soap and gently rub it, rinse it off and dry it with a towel.
Never use abrasive pads, cleaners or ammonia, as this will break down the protective coating on the screen.
In between cleanings, you can wipe down your screen with a dry towel or cloth, just to help remove some of the soot that builds up.  This will make it a lot easier to clean when you do a soap and water cleaning.