How to Dock ArcMap's Table of Contents?

After your grab the TOC, you should see a translucent blue rectangle that represents the new location of the TOC. Drag your cursor over to the left arrow/chevron (either one). The translucent rectangle will change size to show its docked position. Release, and the window should be docked.

When you have grabbed the TOC and see the buttons, drag the TOC until your Mouse is hovering over the Left Button. You will see the shadow appear of the TOC docked on the left side. Then release and the TOC will dock.

The easiest way to dock is double clicking TOC.