Unfortunately, the truck would have a cost basis equal to the basis of the previous owner. If the previous owner used it for business, it may likely have had a zero cost basis to give you.
If the vehicle was not depreciated as a business expense by the previous owner, I would see what they paid for it and use it as your cost basis. If this was the givers' business vehicle, I would guess that they depreciated the basis to zero.
If they used this for business and the previous owner depreciated the vehicle (or if you cannot find out their cost basis) I would recommend using the mileage rate for the truck expenses. You can take the full mileage rate deduction even if the vehicle has been depreciated to zero.