This was the hardest part for me. It took me a bit to figure out what parts were the socket and which was the cable and where were they going to separate. What I did was gently twist the pull tab on the cable in a clockwise direction. This allowed me to see a small separation between the socket and cable. At that point I knew what side of the pull tab I had to use a little pressure on, to continue to wiggle the cable free.
I used this guide to tighten a loose display, and it worked great. The guide is very thorough, so if you follow it step by step you should have no problem. The hardest part was disconnecting the display cable from the socket on the board. Other than that go slow, take your time, and you should be fine.
Removing the display was the hardest part of the whole job. The adhesive is very strong, but just be patient. What I ended up doing was to use the suction cup, the flat end of the spudger, and an iFixit opening tool. I used the suction cup on the screen as directed. Then I placed the flat end of the spudger just a bit into the charging port and held down the phone body by the spudger on my work mat. I pulled up on the suction cup, pushed down on the spudger, and inserted the thin iFixit opening tool in the small seperation. I took my time and worked my way around all of the edges. After that it was really easy. I was able to reuse the adhesive, and my new battery install went just as planned.
Easy to follow guide. Removing the original Apple adhesive is really the hardest part of the entire process.