When you earn CPs and you want to spend them on items and not on credits what do you do? There are two other places on screen you can exchange CPs at but I was wondering about one particular one that gives you items like weapons or trophy ears (eww...) ships and NPCs?
As Ranma says, you need to be outside and not in any rooms, then you will see the listing of ships/vehicles/etc you can exchange CPs for on the normal Exchange CPs page. You just enter the quantity you are exchanging for and it is pretty self-explanatory from there.
It's next to the vehicle or ship, once you are standing outside (not in a room) on a planet. If you are not outside on a planet, you will not see that list!