Step 1: Sand and wash
I don't know that sanding was absolutely necessary here, but in most instances it helps paint to adhere. I used a fine grit sanding pad to give it a quick once over and remove any glue that had previously held the plastic cover. The pad made it easier to get into the holes in the helmet, but regular sandpaper should do the trick.
Once you've smoothed out the surfaces you plan to paint, make sure you handwash the helmet and remove ALL of the dust you've just made. If there is any dust left when you paint, then you'll be painting the dust instead, and it will peel later on. A rag is especially useful to remove any remaining dust and dry the helmet. Make sure it is completely dry before moving on to the next steps.