Carefully begin to close the display until it's at a ~90 degree angle with the upper case.

The hinges should pull out of the case slightly as the display is moved towards the case.

Keeping the display at a 90 degree angle with the case, move the display away from the case while holding the case still, so that the hinges slide out the bottom of the case.

Remove the display.

When you've installed the replacement screen, the MacBook may not boot until you plug in the power supply.