There are two airports in Paris : Orly (south) and Roissy-Charles de Gaulle (north).
Take the RER line B until the RER/metro station "Châtelet". Then change and take the RER line A until "Gare de Lyon" (direction Marne-la-Vallée or Boissy-Saint-Léger). In the Gare de Lyon, take the TGV for Annecy (for the time table, see SNCF).
Take the ORLYVAL which is the train service between Orly airport and the RER/metro station "Antony". The Orlyval leaves every 10 minutes and the journey takes approximately 8 minutes. From the RER/metro station "Antony", the RER line B will take you directly to the heart of Paris. Change in the station "Châtelet", and take the RER line A until "Gare de Lyon" (direction Marne-la-Vallée or Boissy-Saint-Léger). In the Gare de Lyon, take the TGV for Annecy.
You can have a look at the RER map.
You can consult the TGV on-line train timetable (and possibly buy your ticket and reservation) on this site (in english, maybe slow). There is roughly four/five TGVs Paris-Annecy (and four/five TGVs Annecy-Paris) per day. Note that you NEED a reservation in the TGV, but you can buy it (with the ticket) directly at the station on automatic ticket machines if you have a credit card (visa, mastercard, etc..). Of course there are also booking-office windows where you can pay in cash (and have to queue).
The easiest way to come to Annecy from Lyon Airport is to take a direct bus.
Unfortunately, there are not so many.
Booking and timetable: www.altibus.com
Notice that there exists two TGVs connecting directly Lyon airport to Annecy (see SNCF web site).
If you cannot take a direct bus (or TGV) from Lyon airport, the second easiest way to reach Annecy is to take a shuttle Lyon-aiport > Lyon downtown and then take a train at the Part-Dieu railway station.
Information on shuttle timetable and fares can be found on the SATOBUS web site.
You can consult the Lyon-Annecy on-line train timetable on this site (in french, the english version does not seem to work. If asked, Lyon is Lyon-69 or Lyon Part-Dieu).
For those reaching Annecy from Geneva, the most
convenient means of transport (apart from taking a car) is to take the
bus.
Avoid taking the train!
The bus departs from the Geneva Bus Terminal,
timetable available on its
web site
(choose Tickets-Reservation and then Regular Lines Region
Bordercross).
Geneva Bus Terminal is a few minutes from the Train Station (it
is very close to the Main Post Office: click
here for a Geneva map).
In Annecy, get off at the last stop: the Train
Station (see Annecy map: Gare
SNCF).