The answer posted by Akash on Jul 22, 2016 was most useful for me. I did run into something that I wanted to add to what he said, because it seems something has changed with the latest Raspbian update.
After the pi starts booting and you hold shift to enter setup mode, it brings you to a recovery mode GUI. Here you can access the
config.txt file that is mentioned.
I was not able to get anywhere with adding
init=/bin/sh to the end of the file. When I did, the boot would hang.
I had read on some other sites that people were instead adding
single to the end of the file. I tried that and it worked. This time, when it booted, it ended up at a command line (instead of booting into Pixel). From there I did:
and was able to get back to the configuration screen to change my password again.
How I messed up the password is still a mystery, but I think it had to do with using the numeric keypad while typing the password at the command line and it may have had NumLock disabled...
Hope this helps somebody (it'll probably be my future self).