We can reasonably begin to speak of a "scientific method" with the program of the Presocratics, attributed to Thales of Milet in the 6th century BCE.
This program can be summed up in three points:
1) We must cultivate the art of asking questions (a proposition that is not as innocuous as it may seem);
2) We must try to answer them without resorting to myth;
3) Once a consensus has formed around a number of answers, we must look for connections between them, or even common origins.