The original battery was not holding a charge nearly as long as it should.
It went very well in the end. There were a few hiccups. I had good lighting, and some really strong reading glasses. They both helped a lot.
When I removed the battery connector, the "pressure contact" came off. I never got to see how it was supposed to go back on, but on Step 4, the first pic on the left shows it in place as it should be. You can click on the picture (don't just hover, click on it), then click on "View original" at the top left of the image. You can clearly see where the pressure contact goes.
The only other problem, which I hope no one else does, was I MISTAKENLY INSTALLED THE OLD BATTERY INSTEAD OF THE NEW ONE I HAD JUST BOUGHT FROM IFIXIT! Don't to this! I'm so glad I noticed this before I put the cover back on. I'd have been sorely disappointed when the "new" battery performed the same as the old one! Don't get the two batteries mixed up!
A pair of small, spring loaded needle nose pliers made reinstalling the pressure contact possible. I was so glad I had them.