Whenever you write a press release include a link to your charity's website. Many news organisations are willing to link to a charity's website within an online article, particularly if you provide useful information relevant to the topic of the article.
Whenever your charity gets publicity online, check whether the story includes a link to your site. If there isn't a link, email the site asking them to include one. You can track online publicity by registering for free Google news alerts at news.google.co.uk.
Research what sites link to your charity's competitors by running the linkdomain query for your competitor's URL. Then contact these organisations (or directories) to see if they can link to your charity's website as well.
Create a links page where you can add links to partners, suppliers or to sites on related products, services or issues. Offering to post a link on this page will often encourage websites to link to your charity's website.
Be careful who you link to - only link to websites that will be useful to people that visit your site and avoid adding too many links.