If I click on File -> Close, it closes the buffer like I want, but doesn't list a key mapping. What is the key mapping?
BKB has already given correct answer. Just wanted to add that C-h b lists the key bindings applicable in current buffer
C-h b
You can use C-x k to kill current buffer. See Emacs Manual .
C-x k
Well, you can view the shortcut of any function with the Help command (C-h).
Help
Press C-hw and then type the command name as you would in M-x mode.
For example (in your case):
kill-buffer
Hope that helps :)
The question asks how to kill the current buffer. Use M-x kill-this-buffer. On my Emacs, it is mapped to s-k. Fewer keystrokes is better!
M-x kill-this-buffer
s-k
C-x 0
C-x 1