To hide all headers and footers in printouts, you can format the text
contained in them to be hidden (Format>Font>Font tab), and then make
sure that "Hidden text" is cleared on the Print tab of Tools>Options.

But maybe you are looking for a way to suppress headers and footers on
the first page of a document (or section)? Then you can do the
following: Choose File>Page Setup. Click the Layout tab. Enable the
option for "Different first page" and click OK.

Similarly, you can have different content for odd and even page
headers (footers): Just check the option for "Different odd and even"
(File>Page Setup>Layout tab).

For more about sections, headers and footers, see:
http://word.mvps.org/FAQs/Formatting/WorkWithSections.htm