It is quite easy to include a shareThat promotion in a post. To place the fully interactive promotion, simply use the shortcode [sharethat]. The promotion will be rendered 600 pixels wide as illustrated here.
If you would like to render the promotion to appear as the clickable widget image (as it does in sidebars), use the shortcode [sharethat_widget]. As shown below, the promotion will display as the image you have set for the widget, and when clicked will pop up the fully interactive promotion.