If you booked it through a travel agent then you need to call that travel agent. If you booked it through CX's website then you need to call the e-service centre (2747 2200).
Change fees depend on the type of ticket you bought. The very cheapest tickets are not changeable at all. Slightly more expensive ones are changeable for a fee (normally HK$500), and the most expensive ones are changeable free of charge.
There may also be minimum stay requirements on the ticket you bought, and you wouldn't be able to change it if the new date would break those requirements.
Deadlines may also depend on the ticket type, but normally if it's changeable at all then it will be changeable any time up until you take the first flight, and, in most cases, up until the time of the flight as booked for the return.
Remember that there is no guarantee that seats will be available on your new preferred date. CX only makes a certain number of seats available for each fare price level. Getting availability is easier if you have frequent flyer status with the Marco Polo Club, but I guess you don't since if you did you would likely know these things anyway.