Many cats only see their carrier on the way to the vet, so they learn to run when it appears (sample note).
Leave it open in a room your cat likes for a week or two before the appointment, with a worn T-shirt or a blanket inside. Drop a few treats in now and then.
On the day, carry it level with both hands and cover it with a towel in the car. In our cat waiting room, put it on a shelf rather than the floor.