emacs calendar functions

Open the calendar:

M-x calendar

(You can close the calendar with q, which invokes (calendar-exit).

Movement:

• C-f or arrow-right is (calendar-forward-day) and C-b or arrow-left is (calendar-backward-day).
• C-n or arrow-down is (calendar-forward-week) and C-p or arrow-up is (calendar-backward-week).
• M-} or > is (calendar-forward-month) and M-{ or < is (calendar-backward-month)
• C-x ] is (calendar-forward-year) and C-x [ is (calendar-backward-year)
• Use the M-<n> prefix to move a multiple of the above. E.g. M-90 C-f (or M-90 <right-arrow>) moves forward 90 days. (In calendar mode, the meta key is optional, simply 90 <right-arrow> will move forward 90 days, 16 <down-arrow> will move forward 16 weeks, etc.)
• o will let you interactively select a date.
• . will return to today

Other:

• (Right-click on the calendar will generally open up a context-menu about these.)
• p d is (calendar-print-day-of-year)
• TypeC-<space>, move to another date and type M-= to invoke (calendar-count-days-region) (show the number of days between the dates (including the endpoints).
• Type H m or H y to generate an html-format calendar (month and year, respectively). (t <something> generates a number of interesting calendars in TeX, if you are so inclined.)
• Type h to see known holidays for the selected date, or a to see all holidays for the three month period that is displayed. Use M-x list-holidays for even more. Use M to see a list of lunar phases. Use S to see sunrise/sunset information.

Also see the emacs manual.