You can add content to your sidebar sections by using a Widget. Squarespace has pre-configured Widgets for blog archives, recent changes, wish lists, custom HTML content and more.
When logged in click the Structure icon in the admin bar at the top right of your screen.

Important: Pages and Widgets cannot be added to the same section. You can add a new section to your site using this guide.

Hightlight the widget type you would like to add from the list, and click to select and configure.

Fill in the configuration settings, and then click to create widget.
Click to enable the widget on your live site if you're ready for it to be public. If not, just leave it disabled until you're ready to share it with the world.

You can also add widgets from the Administration Area of your site.
Click the Website Management link in the upper left corner of the window, and then choose Architecture under Structure.

Select the section where you would like to add the widget, and then click the add widget button.

Select widget type and configure your widget using Steps 3 - 5 above.