The airport in Vieux Forte is very small and easy to navigate.  Just follow the crowd into the terminal where you'll stand in your first line where you go through Imigration.  They'll check your passport, talk to you briefly, and allow you to pass.  You'll pick up your luggage and go to Customs where they may (or may not) check your bags.  After that, you'll find yourselves outside again, where there are a slew of taxis waiting to pick up people. 

Leaving St. Lucia is not too difficult, but can be a bit odd.  Thanks God the departure tax, that used to be payed in cash in the past, is now already included in the flight ticket, so you don´t have to take care and save cash for it !!!  You'll go through the security check where you end up in the secured portion of the airport.  Several duty-free shops are available within this area, but you will no longer be allowed outside.  Prior to boarding the plane, they will do a pseudo-security check again (on one trip, they only re-checked half of the flight before they started holding things up too much and let everyone else past).