If you haven't booked a transfer, the only way to get to Deauville from Charles de Gaulle Airport is by train with a connection in Paris.
First look for signs in the terminal labeled "RER." These are commuter trains. The Paris direction is Line B. The signs will take you to the train station (the final one). You can buy tickets either at ticket offices with the inscription "Billets Paris et Île-de-France" or at special green-colored terminals. Keep in mind that the latter only accept change and French bank cards. Don't throw it away after passing through the turnstile, it will come in handy on the Paris metro.
Take the Châtelet-Les Halles station, get off and change to metro line 14. Take the train to Saint-Lazare station (the terminus). You can see a map of the Paris metro here.
The TGV Paris-Deauville-Trouville high-speed trains depart from Saint-Lazare station. A round-trip ticket costs 30 EUR (you can book it on the website). Travel time is approximately 2 hours.
Of course, the train ride is long and tiring, especially if you have large suitcases. It is more convenient and faster to get to the resort by cab. A cab from Paris airport to Deauville costs between 300 and 500 EUR + 5% tip. Choose only official carriers. They are easily recognizable by their "TAXI Parisien" checkers.
