Leaving two spaces after colons and periods was a traditional American practice that was followed when monospace fonts were generally used. (A typewriter uses monospace fonts.) The practice helped readers to more easily recognize the beginning of a new sentence.
However, the double space has been made irrelevant by the word processor's modern proportional fonts. With the advent of word processors, monospace fonts have been replaced by letters that do not take up the same space. Further, the interword spacing of modern typesetting software makes today's text more pleasing. In contrast, double spacing can make the appearance of the text less attractive.
The confusion over the issue of spacing persists today because it is correct to use two spaces after a period on a typewriter. A typewriter's characters are monospaced. Each letter takes an equal amount of space. Consequently, an extra space is used after a period on a typewriter to help the reader recognize the beginning of a new sentence. Naturally, persons were taught in typing class to use the extra space. Many of them continue to put two spaces after periods, although they now type on word processors. The result is unattractive.
Today, unless you are using a typewriter or typing in a monospace font, such as Courier, you need only one space after a period. Today's proportional fonts have the extra space already built in. Consequently, adding an additional space is unnecessary.
Therefore, the accepted rule today is to use only one space after a colon, semi-colon, question mark, exclamation mark, quotation marks, or any other punctuation.