What you Need
What to do
Get a cold glass ( you may have to put it in the fridge if your house is warm)
Dilute some washing up liquid in another glass to around about 1 part washing up liquid to 10-20 parts water.
Wipe some of this washing up liquid mixture onto part of your glass, and wait for it to dry - possibly in the fridge so the glass stays cold.
Breathe on the glass around where you added the washing up liquid.
What may happen
You should see that where you didn't put the washing up liquid will fog up, but where you added the mixture stays nice and clear.
Why does it happen?
Your lungs are warm and damp so lots of water evaporates into the air which you then breath out. When this warm damp air meets the cold surface of the glass or mirror it condenses to form liquid water again. Because water molecules are much more attracted to other water molecules than the glass the water tends to form into tiny droplets.
These tiny droplets have a curved surface so as light hits them it will be bent into lots of different directions, scattering it and breaking up the image making it look misty.
The washing up liquid molecules have one end that strongly attracts water and the other end hates it so sticks to the glass. So because the whole surface is covered with water loving washing up liquid, the condensation will stick to the whole of the surface evenly forming a film. This flat film doesn't scatter light in the same way so you can see straight through the water and it doesn't look foggy
Divers use the same trick to stop their goggles misting up. They spit on the inside of the goggles, and some of the protein molecules in your spit act like the washing up liquid allowing them to see easily.