What simple things can a non-commercial, voluntarily-run community or hyperlocal website do to improve their ranking on Google?

In addition to what said, it looks like encouraging more participation through commenting and subscriptions could also help.  These factors are signals of popularity which will help SEO.  Take a look at the site in Google search using the following command: site:http://alittlebitofstone.com - you'll see that Staffordshire is not appearing on interior pages.  If you want to rank for that term you'll want to include it more often.  You might see some additional hints as well.  On the home page, if you want to rank for "Stone Staffordshire" those terms need to be placed more closely together or next to one another.  The sites that rank above have them together.  Lastly, you're going to want inbound links to the site.  This is easier said than done but links also convey popularity and encourage crawling the site by search engine bots.  Try contacting the sites in your blogroll since you're already linking to them.  You're on the right track and have a nice looking site. Good luck!

Some great advice here already, but I'd add a few things: 1. Don't expect to rank for "stone." It's irrelevant. Users searching for that term could have a number of intentions, like looking for a type of stone or perhaps that's the name of a movie or celebrity. Your site won't be able to compete in this space and shouldn't need to either. 2. Sounds like this is something that a community can really get behind. Setup a Facebook page and Twitter account. Advertise this on your site and gain followers/likes. This will spread awareness and naturally build links for you. And this will help boost your visibility in search results.

Do what Paul and Jon have said. Also, for a boost, buy http://StoneStaffordshireNews.com so you have the keywords in your URL. Despite what many people are saying, tests show that having the keywords in your domain name still helps a lot. So buy that domain. Move your content onto that domain. Do a 301 redirect from http://alittlebitofstone.com to http://StoneStaffordshireNews.com. That way: 1. Google will transfer all or most of the SEO value you've built up in http://alittlebitofstone.com to your new domain, and 2. anyone who knows you by your old domain will still find you by going there (they'll just be transferred to your new domain). Also, send strong geographic signals to Google. There' s a meta file, don't remember the name, where you can declare your geo location. And you can put up a Google Plus Local page and link it to your website. So you're sending strong signals that you are local to that place. Good luck.

I'd add "Stone, Staffordshire" to the page Title tage, and the <meta name="description" > tag in the HTML for a start — I'm not sure how much truck Google holds with either any more, but it can't hurt. As the site is Wordpress, the All in One SEO Pack plugin makes editing those bits pretty easy — and will also attempt to improve SEO for individual pages and posts (it will populate with tags, but you can hand edit). Google is increasingly basing all searches more and more on local results — so some geotagging of the site and also individual posts may help. On BiNS i use a plugin called Geo Mashup for individual posts, and have a "site wide" central-Birmingham value encoded into the theme for the front page  (here's a quick guide http://www.problogger.net/archives/2008/04/15/geoblogging-how-to-geotag-your-blog/).