At the bottom of the phone there's a dark plastic piece with 4 Phillips #00 screws in it. Remove these 4 screws and then carefully pry out the plastic piece to access the display connector.

Helpful hint: When removing delicate screws, you can stick them to a piece of tape in roughly the places they'd go back in. This helps you remember what screw goes where, in case any of the screws are slightly different sizes.

Once the black plastic piece is free, first unplug the battery connector (connector highlighted in red in the second photo on this step, on the bottom right). This may have unplugged itself when you lifted the black piece, but if not it's a good idea to unplug it before continuing.

Now unplug the display connector (connector highlighted in blue, on the bottom left). You can lift it up and carefully unplug the display connector (connector that comes in from the left side) with a small spudger. These connectors are extremely delicate, be careful not to damage the connector on the phone's circuit board.

You don't need to unplug any of the other connectors, but if one comes loose make sure it gets plugged in. The battery connector won't plug in anywhere else but it's possible to plug the antenna connectors into the wrong ports if you're not careful.