Right-click on the Start Button on your Taskbar, choose Properties, and then
click on Customize.  Put a checkmark next to "Enable context menus and
dragging and dropping".  Click OK to close the window, then click Apply and
OK.

What items?
Right click and "Remove..." works for the items on the left.

Fro the others:
Right click Start button
Click Properties
On the Start Menu tab click Customize.
You can select what you want from there.

Apito

If you are removing items like folders, you may have to delete the contents
first..