It’s essentially a 2-step process:
1. Upload the icon image(s) to your media library.
2. Add a “Text” widget to your sidebar and insert code similar to the following:
<a href="https://twitter.com/bledsoe"><img src="https://www.lancebledsoe.com/wp-content/uploads/2009/07/tweeter_48x48.png" /></a>
<a href="https://www.facebook.com/lancebledsoe"><img src="https://www.lancebledsoe.com/wp-content/uploads/2009/07/facebook_48.png" /></a>
<a href="mailto:[email protected]"><img src="https://www.lancebledsoe.com/wp-content/uploads/2009/07/email_48x48.png" /></a>
<a href="https://www.lancebledsoe.com/feed/"><img src="https://www.lancebledsoe.com/wp-content/uploads/2009/07/rss_48x481.png" /></a>
Then just change the URLs so that they point to your icons and links. As you can see, I have four icons in my sidebar (twitter, facebook, email, and rss).