The columns on either side of the main body of the site are called sidebars. There is a left sidebar and a right sidebar.
All of the information in the two sidebars are "blocks." You can access the blocks under the administer menu (/admin/build/block).
You can control where the blocks will show. Most often you're going to use the left or right sidebars.
You can also control in what order the blocks show up in based on their weight -- smaller items float to the top.
You can use the blocks already created for you (such as search, log-in, etc.), or you can create ones of your own.
Choosing when/where the blocks show up
You can also control when/where the blocks will show up. This is handy for when you want an item to show up only on specific pages, such as a table of contents for your monthly newsletter.
Click configure next to the block you want to edit, Scroll down. Towards the bottom are "Page specific visibility settings" where you can choose when and where the block shows up.
Drupal 5 screenshot Drupal 6 screenshot
Save the block.