If you love watching creative makers do their thing, I highly recommend you watch Aaron Draplin (creator of Field Notes notebooks) go through how he goes about designing a new logo.
In the video he is challenged to design a logo for a concrete foundation company. He starts with pencil and paper and sees what the letters suggest. Then he digs through some old design and corporate identity books. Once he has several pages of ideas he gets on a computer and starts working the logo up in Adobe illustrator.