The area51 page of beta sites show several statistics about how well a site is doing. Are there any general advice or guidelines on how a site's community can improve those numbers during the public beta period?
I think all the metrics listed can be improved by one thing: More Users
More users directly influences
Questions Per Day and
Visits Per Day, which gives the experts a reason to come to the site regularly to answer questions, which will increase the
Active Users, and
So providing SE is OK with us advertising beta sites, go out there and advertise your site!
In addition, be mindful of how you treat new users of your site. They might not understand the scope of the site, or if they're new to SE entirely they probably won't understand downvotes or votes to close, so be a bit more understanding with them.
If they ask an on-topic question that is badly worded, edit it into a good one. If they ask an off-topic question, simply vote to close and leave a comment about why it's off-topic (don't downvote). You want new users to keep coming to SE with their questions, and to perhaps one day become a contributing members of your community.
Remember, you need users to ask questions before you have a reason to need experts.