FYI there are 14 screws - not 13
This bit really is tricky. Just be patient and make sure you don't pull the orange cable strip off the black plastic connector which attaches to the hard drive. You can try using a thin (preferably plastic) lever to work the black connector away from the drive to reduce the stress to the orange cabling.
As another reviewer suggested you don't need to unplug the 2 cables for the mic and power cables and risk breaking the connectors. Once you have managed to unclasp the casing just - carefully - put the casing to the left side and prop it up so it's standing almost vertically. You will have enough room to access the hard drive underneath.
As suggested above this is quite tricky due to the plastic catches towards the front of the case (ie where the trackpad is). Access the front 2 on the right by going in through the empty battery slot and prise away the plastic from the case. That leaves the 2 on the left which are tricky. Use a spudger or flat head screw driver (v careful here though so as not to scratch the casing) to work around the front left casing. Don't give up or despair - it does unlock eventually!
Make a full page printout and using sticky tape put the screws (in clusters if easier) where they should go on the photo. In fact I took a blank sheet of paper and did a step by step guide to all screws I took out and then put the screws next to each step header (1,2,3....) and put sticky tape on them.
To be clear on this step you don't need to remove the long black screw (in fact it doesn't appear possible to remove it completely) just make sure it's been unscrewed as much as possible and then leave alone