Depending upon the Theme you have chosen, many of them come with the calendar in the Theme just commented out. Open the
sidebar.php and look to see if the code for the calendar is there and then remove the comment codes and it should show up.
If not, then copy the calendar code from the Default Theme and paste it where you want it in the
sidebar.php template file and then copy the styles from the Default Theme style.css and paste them into your Theme's style.css. You can tweak it from there to match your theme.
Currently reading information can be found at Using_Custom_Fields.
If there is a positioning problem with your sidebar, it is because there is 1) something in your sidebar that is pushing the width of the sidebar out too far to fix in the space provided like a link or image, 2) there is something in the main content section that is pushing the sidebar down that is too wide like an image. Isolate what it doing the pushing and shoving and either make it smaller or resize one of the parts and pieces.
Here are some links that will help you:
Customizing Your Sidebar
Stepping Into Templates