Search engine optimization and social media integration are huge topics in their own right, but there are a many optional WordPress plugins that will help you achieve the basics.
The two I recommend are:
- Jetpack, a bundle of optional features from the makers of the WordPress software (and the operators of WordPress.com). Jetpack offers a number of features to help speed up and secure your website. In addition, you can turn on an option for displaying social sharing buttons for Twitter, Facebook and other social sites. You want to make it as easy as possible for website visitors to share your content.
- Yoast SEO, one of the most popular search engine optimization plugins. Yoast also includes features for optimizing how your content is seen on social media. It will show you a preview of how your content will be displayed in search results and social media. You can alter that default presentation to include a different image, headline, or text snippet than each service would use by default.
Note that Jetpack and Yoast SEO are both offered as free plugins, but with an upgrade path to paid enhancements. Particularly for a volunteer, nonprofit website, my advice is to see what you can do with the free versions before you even think about paying for extra bells and whistles.