Display day-in-year (calendar-print-day-of-year).
Regenerate the calendar window (redraw-calendar).
Scroll the next window (scroll-other-window).
Exit from calendar (exit-calendar).
To print the number of days elapsed since the start of the year, or the number of days remaining in the year, type the p d command (calendar-print-day-of-year). This displays both of those numbers in the echo area. The number of days elapsed includes the selected date. The number of days remaining does not include that date.
If the calendar window text gets corrupted, type C-c C-l (redraw-calendar) to redraw it. (This can only happen if you use non-Calendar-mode editing commands.)
In Calendar mode, you can use SPC (scroll-other-window) to scroll the other window. This is handy when you display a list of holidays or diary entries in another window.
To exit from the calendar, type q (exit-calendar). This buries all buffers related to the calendar, selecting other buffers. (If a frame contains a dedicated calendar window, exiting from the calendar iconifies that frame.)