how to translate this slogan '向前一小步，文明一大步' and the like in almost every public toilet in China
The quote from your title:


  '向前一小步，文明一大步。' 


which literally translated to: "One small step forward, (is a) big step for civilization"

Is kind of a paraphrase of Neil Armstrong's "One small step for a man, one giant leap for mankind" which translates, according to Wikiquote, to:


  '这是我个人的一小步，却是全人类的一大步。'


However, as mentioned above, this is a euphemistic way of asking people to get closer to the urinals in order to keep the floor dry and clean.