Sometimes we do not really have a choice on how we dry our hands in public restrooms. However there are two main methods: paper towels and air dryers. The video below by ASAP Science gives a 2 minute summary about the pros and cons of both in terms of environmental and hygienic benefits. Would you rather dry your hands with paper towels or air dryers?
Things to consider: deforestation, saving paper, waste produced by man, hygiene, bacteria, convenience, whether or not the air dryer is a Dyson Airblade (because they are awesome!).