Depending which ship it is it'll either be available from the ship vendor at Eart Spacedock or you'll have to claim it from the CStore directly, you can then switch ships at the shipyard at Spacedock, K7 or DS9.
Without checking in game it's the Excelsior R, NX Class and Oberth that have to be claimed from the store, everything else should be unlocked at the ship vendor for you to claim.
there are two guys standing in the open part of the shipyard. one is for the tailor (use him if you buy a costume) and the one opposite is where you change your active ships, all new one should go there assuming you have a ship slot avialble.
some do have to be claimed via the ship requisition officer inside the shipyard itself. i think its pretty much the nebula for that one.