This is something that your server 'ought' to send across in the HTTP Headers as our spider connects to your server. On Apache, this will usually work by default if you have true HTML pages. If it goes through the PHP interpreter (uses PHP code) it will not report this information and you will see the error about not supporting Last-Mod.
I have written a script that will get you most of the way there...
ServHead is what I call it. What it does is to read the lastmod time from the file on your server and insert it into the HTTP headers for your webpage.
While this code was originally taken from some long-forgotten two-liner as an example on someones website, it has been reworked a number of times to help improve it and round it out some.
It is setup as-is to work with static files written in PHP, but could easily be converted for template system that creates pages entirely from your database as long as your CMS has a database field for when a document was last modified. The code is commented where you would need to add logic to check your database.
This script also helps your pages to support the If-Modified-Since header that Google uses to skip a page that hasn't changed since their last check. This saves both you and them some bandwidth and allows them to check your next URL on their list a little sooner.
In order to use it, include it as the first line of your code before anything is output to the browser (including empty spaces) such as...
<?php include("servhead.php");?>
You can use the
HTTP Header Checker at AutoMapIt to see if your headers are coming out properly and using the Last-Modified header.
Of course, if you want the benefit, but don't want to deal with the particulars of getting this setup correctly, I can always install it for you for a small fee.
Google Webmaster Guidelines does suggest that your server should support the Last-Modified and If-Modified-Since headers, but I don't exactly see better ranking from doing this all by itself. What I do see is reduced bandwidth and faster indexing/re-indexing of your site since many pages wouldn't be updated regularly and Google can just skip those to get to the ones that have considerable amounts of fresh, new content quicker and easier.