How do you properly reinstall the Intel HD graphics driver?

Device Manager, expand Display adapters, right click the Intel HD entry and Uninstall device. Tick the box to delete the driver software for this device, then reboot. Windows comes back on the basic display driver (low res, that's expected) and usually pulls a driver from Windows Update on its own after a few minutes. The bit that catches people on laptops: the generic Intel installer sometimes refuses with a message that your computer doesn't meet the requirements, because the manufacturer ships a customised version. If that happens, grab the graphics driver from your laptop maker's support page for your exact model instead.