I've done some research on the Web, but can't seem to find clear information on
transport from the airport to places the various ferries depart from, and where
to book the ferry tickets (I'm resisting the urge here to say, 'It's all Greek
to me.')

Buses leave right from the airport for Piraeus, the ferry port for
most Greek Islands. It's no problem at all to get bus tickets last
minute, but do leave extra time before your ferry leaves - the ride
can take more than an hour due to traffic, you might have to wait in
line to buy your ferry ticket, and the port area is poorly labeled and
very confusing and it can be tricky to figure out exactly where to go
(30 ferries to all over leave from the same place).

If you go into Athens for a few hours, you can get the metro to
Piraeus.

Anyway, has anyone ever gone from the Athens airport to and of the Greek
Islands by Ferry? Any advice? Ideally I'd like to be able to book a driver to
meet us at the airport to take us to the correct dock, book the ferry tickets
and a return by plane. I have numbers for a couple of Greek travel agencies in
the US, but I'm not sure if an agent would want to bother with such a small
portion of the arrangements. Thanks for any advice!

You can buy ferry tickets at the Athens Airport. Ferry fares are
fixed by Greek law, so it doesn't matter where you get them.

It's normally no problem at all to get on a ferry, but if you want a
cabin, or if you're going in absolute peak season, you might want to
try to reserve in advance.

You don't need a driver to get from the airport to the ferry port; the
bus gets you right from one to the other. If you want to spend a few
hours in Athens before your ferry leaves (i.e. see the ancient sites),
then take the bus to the port, store your things in temporary storage
there, take the metro to the ancient sites, and then take the metro
back to the port.