Grasp the broken vertical blind slat (which is probably on the floor) and examine the top hole. If any of the broken material remains attached to the slat, trim it off using scissors so that the repair device will fit flush with the surface.
Pick up a metal vertical blind hole repair device and turn it so that the open side faces the slat.
Push the device downward over the hole, making sure to align the hole in the device with the hole in the slat. The two sides of the device open as you push it down so that the slat fits inside of it.
Look up into the track mounted at the top of the window or door. Locate the small stem that does not have a slat hanging on it. Use a step stool so you can access the area if needed.
Raise the repaired hang hole up to the hooked part of the stem, and then place it over it to rehang the vertical blind slat. To insert the slat into stems without hooks, simply push it up in the bottom of the stem until it remains securely in place.