You may want to remove either the keyboard or the lower case to access the display signal connector. I can't say with confidence which one, but I'm going to guess lower case. Use a #0 Phillips screwdriver to remove the screws from the bottom of the laptop, keeping track of where each one goes and how long the individual screws. The display signal connector is a long, flat connector, and it often has a dull, woven wrap around the individual wires to protect them as it snakes into the display.
Again, I'm not sure if your laptop has a ZIF connector or a standard insertion force connector, so I'll detail both.
If you have a ZIF connector, use a spudger to lift the release mechanism, and the cable should come out with little to no resistance. When reinstalling the cable, make sure that you lift the release mechanism before sliding it in, then lock it in place.
If you have a standard insertion force connector (almost like a block connector, except it's way smaller), then wiggle the connector loose; be careful not to separate the connector block from the wires as you're pulling. You shouldn't have to force it, but you'll need to apply some pressure to pull it out.