Answer to question: http://www.awpcp.com/forum/viewtopic.php?f=4&t=5180&start=10

widget-search.snippet.php

<?php

echo $before_widget . $before_title . $title . $after_title;
echo '<div align="center">';
echo '<form method="post" action="'. url_searchads() .'" onsubmit="if (this.keywordphrase.value == \'Search by keyword\') { this.keywordphrase.value = \'\'; } return true;">';
echo '<input type="hidden" name="a" value="dosearch"/>';

$keywordphrase = stripslashes_deep(awpcp_post_param('keywordphrase'));

if ($instance['show_keyword'] == 1) {
    echo '<label for="awpcp-search-keywordphrase">' . __('Search by keyword', "AWPCP") . '</label><br/>';
    // if keywordphrase is empty, the place holder string is printed as the field's value,
    // otherwise the value entered by the user will be printed.
    if ( empty( $keywordphrase ) ) {
       echo '<input id="awpcp-search-keywordphrase" type="text" name="keywordphrase" value="Search by keyword" onblur="if (this.value == \'\'){this.value = \'Search by keyword\'; }" onfocus="if (this.value == \'Search by keyword\') {this.value = \'\'; }">';
    } else {
       echo '<input id="awpcp-search-keywordphrase" type="text" name="keywordphrase" value="' . esc_attr($keywordphrase) . '" onblur="if (this.value == \'\'){this.value = \'Search by keyword\'; }" onfocus="if (this.value == \'Search by keyword\') {this.value = \'\'; }">';
    }
}