The golden hand with attached Sun is pointing somewhere into the first quarter of the area of the sign of Capricorn, closer to the sign of Sagittarius than to the sign of Aquarius.

We add therefore about a week (7 days) to the beginning of the sign of Capricorn, and the result of December 29th (22+7) gives us the correct date.

Remember that we had to make an estimate where within the area of a sign the golden hand is pointing to. This estimate will not always be accurate and we may get an incorrect date by a day or two.  

The date of December 29, 2010 was chosen randomly to demonstrate how the current date can be read. Other dates can be read from the Orloj in a similar fashion.