If this is your first international flight, you'll need to fill out a declaration form upon arriving in St. Lucia. The form ask a few basic questions such as the purpose of your trip, and where are you staying. If you don't know the address (and you most likely won't) list the area, such as CoCo Palm Hotel, Rodney Bay.
You'll need your passport number, so have it easily accessible while your on the plane. Have your own pen or a few pens (if you are traveling as a family) to make life simple.
The customs officer after your arrival will collect the form and your passports (children included).
For details on what you can bring into St. Lucia, see the Customs & Excise section.