Actually, the posters are wrong - the water is only to rinse (that is what we were taught, anyway). A little soap with some water in your hands first, then wash as if you were putting on lotion, getting in between your fingers, washing right up to your wrists - to get the gunk under your nails, you rub your fingertips in the palms of your hands, pushing the skin away from the nail gently (do not rub the fingernails on the skin, to prevent scratch injury). Do that for 20-30 seconds. The rinse water should be tepid, which will keep your skin from being damaged (really warm water will dry out/burn your skin, cold could damage it).
Use a paper towel to turn off the water taps once you are done - otherwise, if you have to touch it with bare hands, you have defeated the purpose of washing your hands. If coming out of a public washroom, probably a good idea to use a paper towel on the door handles as well.
When I was taught how to do the hand washing thing, we started out with a soap that had sparkles in it - if you got every sparkle, then your hands were clean. Not something you want to use every day, but it is a good trainer.
I would recommend something like "Dove" soap, or one of the Aveenos, to decrease the drying out of skin. Using a hand lotion occasionally to keep your hands from over drying and cracking is recommended.
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People think there are four elements to the world; fire, wind, water and earth. They are wrong. There is a 5th element - surprise. - paraphrasing of Terry Pratchett "The Truth"