The most easily described way.
Go out the south airport exit. Get on Toll 417 west. Then Look for the exit with either or both 535 or 536 on it and take that exit. Follow the signs for 536 west and you will cross over a big freeway (I-4) and then see the Disney welcoming arches. Skip the first little exit after the arches (Downtown Disney) and then watch for signs coming up fast for Port Orleans, I think the third little exit.
Bring plenty of quarters for tolls. Note that some toll plazas require that you take what looks like an exit ramp to pay your toll (in cash), then you merge back onto the highway main lanes.