Move the poinsettia to a table. Place it on a towel to prevent any water stains from forming on the table. Make sure you have bright and adequate light so you can see all areas of the plant.
Inspect the poinsettia. Ensure that the stains or spots you can see are, in fact, water stains. Use a magnifying glass to verify the spots aren't signs of plant disease, decay or even microorganisms living on the plant. Look for bumpy textures, flecks of color or depth to the spot. Once you're sure the spot is just a water stain, you can work on removing it.
Take one of the soft cloths and dip it in to the room-temperature water. Wring out the excess water until the cloth is just damp. Hold the leaf or bloom in one hand and use the damp cloth to gently rub the spot on the plant. You may need to re-wet the cloth if the stain is large. Work with only one leaf or bloom at a time. Visually inspect the area to ensure the stain has been wiped off.
Use the remaining dry cloth to go back over the same leaf or bloom to gently hand-dry the area. Make sure to use soft, circular motions so you don't damage the plant. Repeat the process for every leaf or flower with water stains.