Do blogs really work to keep people informed of your ministry? If so, what's the best way?

Yes! 

Blogs allow your readers to comment and interact with you. It's let formal than a website and your readers can stay informed of the updates via RSS feed (http://www.whatisrss.com).

Update often; let your followers hear personal stories about what is going in your ministry. Keep the postings shorter and add pictures to create a deeper level of connection with your readers. 

Keep your blog simple, clean, and easy to read. Don't overpower your readers with too many graphics and a distracting background.