Thanks for the reply. What I ended up doing was purchasing the book Professional SQL Server 2005 Integration Services. I found the answer in there, but I ran into a new problem that doesn't seem to be addressed by the book.
Initially after running my package, I got an error on a couple of my fields stating that an unicode string could can not be convert to a non-unicode string. I solved this issue by changing the datatypes in my database from varchar to nvarchar.
However in the near future, I am not going to have a choice to change the datatypes in the database. Is there another way of handling situations like this within the package itself?