Heat the flat iron a little, or heat it and leave it to cool. It should be warm, but not too hot to touch. Unplug the flat iron before you begin cleaning. Dampen a small terrycloth towel with warm water. Don't use water that is either very hot or very cold - it must be lukewarm only. Using one finger, gently rub one plate at a time where the grime is. Avoid harsh scrubbing on the ceramic plates, to avoid scratching them. Wipe down the plates until there is no more buildup on them. Check to make sure you've reached down to the bottom (closer to on/off switch and settings) and removed any gunk from there, too. You can use a cotton swab if it's too hard to get the towel into corners. Clean off any residue around the sides or edges. Use a fresh surface of the towel as necessary.
Belinda