To use this on an iOS device with Voiceover, double-tap-hold to enable gesture passthrough. Then drag up, left, right and down to move within the current month. Swipe up and down to go to the previous and following month. Swipe left and right to go to the first and last day of the current month. Double-tap (tap) to select a date and Triple-tap (double-tap) to simulate the dismiss event.
To use with the keyboard use up, down, left and right arrow keys to move within the current month. Use page up and page down to move to previous and following months. Use home and end to go to first and last day of the current month. Use enter to select a date and esc to simulate the dismiss.
Mouse and touch can be used as you would expect them to be used.