Remove the four indicated Phillips screws from the front wall of the battery compartment. When working from the left, remove the 2nd, 4th, 7th and 9th screws.
Four 3.25 mm Phillips #000. (Head: 4 mm. dia. x 4mm thick)
There's a trackpad and keyboard ribbon cable connecting the upper case to the logic board, so don't pull the upper case off entirely just yet.
Use a plastic opening tool, an expired plastic credit, or a similarly-thick card to pry up on the upper case, starting in the upper-left corner and working around to the front of the computer.
The upper case is likely to stick at its connection above the front edge of the optical drive. If this happens, first free all other sides, then proceed to pull upward on the upper case from either side of the optical drive opening. Here again, inserting a plastic card, guitar pick, etc. can be useful.
If you stand the base of the MacBook on one end to get a better look, you may displace the four grey plastic clips that hold the right side of the upper case in place. Don't panic. They slide into slots at the top rightmost edge of the lower frame, above the front edge of the optical drive.
During reassembly, make sure the clips on the right side, above the optical drive, click firmly into place. They're different from the clips on the left side, and so normally they require a little firmer pressure to click into place.
While holding up the upper case, pull up the black tab on the connector end of the silver ribbon cable away from the connector's socket on the logic board.
If there is no black tab, you can also use a spudger to gently pry the connector out of its socket on the logic board. This connector is tall, so be sure to pry straight up.
If you happen to break your upper case cable when removing the upper case, we stock the cable individually and we have a guide that makes replacing it easy.
While you have the upper case removed, it's a good time to remove dust, hair, etc. It's best to use a can of compressed air, though if you use a brush, make sure that its bristles are made of a material (usually animal hair) that doesn't generate static electricity, which can destroy electronics.
Upon reassembly, there are 4 grey plastic clips installed in slots running along the top of the frame in front of the optical drive (refer to second and third pictures). These clips must be installed in their slots for their mating tabs on the underside of the right side of the upper case to snap into them.
Use a spudger to move the gray display data and black speaker cables to the right. This will reveal a silver screw securing the fan housing to the lower case.
My wife's MacBook has been overheating for some time, and then shutting itself down. Your instructions were great, but I did note that I needed to unscrew the cable tie near the speaker in Step 17.
The system had some dust in it, used the air can to spray it all out. Dust was on the heatsink vents, too. Closed it all up, and peak temps during a software install that crashed it three times yesterday was 145F - yesterday it was passing 170F and crashing.