There are sharing icons you can enable including a Pinterest one to display at the bottom of your posts by following this guide. http://en.support.wordpress.com/sharing/ When you use the Pinterest sharing button on a post, it opens up all images in that post, with the titles below them, so you can select which to pin, and there's typically a pin for the post itself as well that shows the author Gravatar.
You can capture an image of a Pinterest icon and upload it, link to it and display it in a text widget. I have done this here in the text widget at the top of my sidebar for those who want to follow me on Pinterest.
For creating links in a text widget see:
You can upload image files by clicking the Add Media button right above the editing area of a page or a post. http://en.support.wordpress.com/add-media/
You can also upload new files to your Media Library using Media → Add New. http://support.wordpress.com/media/media-add-new
See also http://wpbtips.wordpress.com/2009/04/26/images-the-three-link-options/
For troubleshooting see http://en.support.wordpress.com/images/troubleshooting-images/
This support doc explains how to embed from Pinterest http://en.support.wordpress.com/embed-from-pinterest/
This one is for Pinterest site verification http://en.support.wordpress.com/webmaster-tools/#pinterest-site-verification
NOTE: Be mindful that some people do not want their original images shared on internet bulletin boards and have copyright licenses that prohibit their sharing.