Structure your theme so you start the <body> in the header and you close the </body> in the footer (same thing for the <html> tag):
header.php
<html>
...header content
<body> <!--- body is started in the header, used on every page -->
index.php, page.php, single.php, home.php – etc
...content
footer.php
...footer content
</body> <!-- body is closed in the footer, also used on every page -->
</html>