If you are not staying at the resort (here, Caribbean Beach) that night you would just go to a Mears counter at the airport and they will sell you a shuttle ticket for going to the resort.
Although Mears' shuttle does not officially take reservations to and from Disney's resorts, you still have to call them at least 24 hours in advance to arrange a pickup time for going back to the airport. If you are not staying at the resort the night before, give Mears a call the day before anyway to see what they can do for you.
(copied from another post) If you are touring with friends staying on site but not staying with them, there is a chance they can put you on their room reservation for the night before you all go home. Then they can book Magical Express for you.
Do not rely on will-call at bus time for your ticket back to the airport. Get written confirmation of that trip as soon as it is available even if you have to miss a rope drop or report back to a resort in the mid-afternoon.
Get in the right car! Ask the driver and show him your ticket or reservation number if you are unsure. The vehicle you are assigned to may or may not have Magical Express markings on it.