To use the format painter, select a cell that has special formatting, click on the "paint format" button from the toolbar and then select one or more cell to apply the formatting.
Microsoft offers an example to show why this feature is useful:
"Say you've written a report in Word. You like the look, especially your headings, which are 14 pt. Bookman Old Style, centered, green, and bold, with a nice subtle shadow. Fifteen minutes before you're supposed to present the report to the team, your manager asks you to add four new sections to the report. You spend thirteen minutes adding the information, and the next two wishing that you hadn't chosen such complicated formatting for your headings, since you now have to apply it to all the new ones. Using Format Painter saves you that time and duplicated effort. Instead of having to manually apply the font, font effects, centered paragraph alignment, and other formatting to each new section heading, you can quickly copy all of the formatting attributes by using one toolbar button."
Unfortunately, format painter is not available in all Google Docs applications and you can only use it in Google Spreadsheets. So much for the Google Docs consistency.
{ Thanks, Cougar Abogado. }