I purchased the limited edition and I have access to the original constitution class but I don't know how or when I will have access to it, can anyone help?
The special unlocks are generally available from the C-Store. Click on the down-arrow next to the minimap to access the C-Store, and you should see a tab for 'Unlocks'. "Purchase" the Constitution if its there. You'll then need to talk to a guy in the Shipyard, as mentioned, to make it your active ship.