Example:
// create a nonce in a form
<form method="post">
<!-- some inputs here ... -->
<?php wp_nonce_field( 'name_of_my_action', 'name_of_nonce_field' ); ?>
</form>
// validate the nonce
if ( ! isset( $_POST['name_of_nonce_field'] )
|| ! wp_verify_nonce( $_POST['name_of_nonce_field'], 'name_of_my_action' )
) {
print 'Sorry, your nonce did not verify.';
exit;
} else {
// process form data
}