Open the package in BIDS, change the Connection Managers to point to the new server and database and then save it back to the original location where it is referred to for execution.
If you want to make this a little easier in the future implement a Package Configuration that would allow you to change where the Connection Managers are pointing without having to modify the SSIS Package itself. You can find information about "SSIS Package Configurations" in SQL Server Books Online.
There are no special teachers of virtue, because virtue is taught by the whole community. --Plato