if(isset($_POST['submit'])) {
    // define the list of fields
    $fields = array('name', 'address', 'city', 'state', 'zip');
    $conditions = array();

    // loop through the defined fields
    foreach($fields as $field){
        // if the field is set and not empty
        if(isset($_POST[$field]) && $_POST[$field] != '') {
            // create a new condition while escaping the value inputed by the user (SQL Injection)
            $conditions[] = "`$field` LIKE '%" . mysql_real_escape_string($_POST[$field]) . "%'";
        }
    }

    // builds the query
    $query = "SELECT * FROM TABLE ";
    // if there are conditions defined
    if(count($conditions) > 0) {
        // append the conditions
        $query .= "WHERE " . implode (' AND ', $conditions); // you can change to 'OR', but I suggest to apply the filters cumulative
    }

    $result = mysql_query($query);

        <form method="post" action="">
            <tr>
                <td>Name:</td>
                <td><input type="text" name="name" /></td>
            </tr>
            <tr>
                <td>Address:</td>
                <td><input type="text" name="address" /></td>
            </tr>
            <tr>
                <td>City:</td>
                <td><input type="text" name="city" /></td>
            </tr>
            <tr>
                <td>State:</td>
                <td><input type="text" name="state" /></td>
            </tr>
            <tr>
                <td>Zip:</td>
                <td><input type="text" name="zip" /></td>
            </tr>
            <tr>
                <td>&nbsp;</td>
                <td><input type="submit" name="submit" value="Search" /></td>
            </tr>
        </form>
    </table>