It should be one space after a period — period.
The only reason why some people, particularly older people, use two spaces after a period is because they grew up using typewriters. Your computer teachers in middle school also probably taught you the typewriter method since that's all they knew.
Typewriters had what were called "monospaced" fonts, meaning that every character takes up the same amount of space. Since all characters were the same width, you needed two spaces after periods to help break up your sentences.
With computers, each character has a different width. The W is considerably wider than the I, the m is wider than the l, and so on. Therefore there is no longer a need for the extra space after periods.
