You can use a soft brush to gently remove dust from the surface of comics. For stubborn dirt, a mild cleaner made for delicate materials might do the trick, but be sure to test it on a small area first.
Well, cleaning comics requires a bit of care. Start by placing the comic on a clean, flat surface. Use a microfiber cloth to wipe away any loose dirt. If there are stains, you could try a gentle solution of water and a tiny bit of mild soap, but make sure to rinse it off thoroughly to avoid any residue.