I was very surprised by how much heat I needed to apply to loosen the glue. I used a blow dryer and then heated up a rice-filled pillow-thing I use for sore muscles. I put that inside a plastic bag to avoid the moisture and pried while phone sat on that. It was hotter than I would normally make it for muscles! But that did the trick. Still had to pry pretty hard and it finally let go with a bit of a snap. I just pried with a spudger at the open space along the left side of the battery, about mid-way up.
Ditto the comments by Salta. I compared the iFixit battery cable to the battery cable of the one I had removed and found that I needed to kind of crimp the cable a bit where it needs to fit between the battery and the connector. It's all quite stiff. Make sure the connector snaps into place!
IMPORTANT TO NOTE: The top of the screen is attached to delicate cables inside the phone! Pull up carefully and keep a hand on the top of the screen so it doesn't pop up.