Once the connector has been released, pull the home button end of the assembly away from the rear case, using the top of the phone as a hinge.

Open the display to about a 90º angle, and lean it against something to keep it propped up while you're working on the phone.

Add a rubber band to keep the display securely in place while you work. This prevents undue strain on the display cables.

In a pinch, you can use an unopened canned beverage to hold the display.