The event when a laugh arrives at Never Land and bursts into a new fairy or sparrow man is known as an Arrival. Every Arrival is attended by any fairy or sparrow man who can make it, who hopes that the new fairy will belong to his or her own talent group. Arrivals happen a bit differently in the books and movies.
In the movies (Pixie Dust era)
The laugh that would become Tinker Bell arrived in Pixie Hollow upon a dandelion seed. Fairies escorted and guided the laugh to the Pixie Dust Tree, where dust-talent sparrow man Terence sprinkled a cupful of dust on it. The laugh transformed into a new fairy, and the dandelion seed became her Arrival Garment. A series of mushrooms popped up in a circle, upon which fairies of assorted talent guilds placed objects representing their talents, which floated just above the mushrooms. Upon touching objects that didn't correspond with her talent, the mushroom ceased to glow and the object dropped or dissipated, depending on whether it was solid or otherwise. When Tinker Bell touched the tinker's hammer, it glowed brightly, showing that she was a tinker fairy. She was then given her name by Never Land through Queen Clarion.
For Periwinkle, her laugh likewise came upon a dandelion seed. But it took a different route, crossing over into the Winter Woods. It drifted under the stream of pixie dust flowing from the root of the Pixie Dust Tree that extended into the Winter Woods. As with Tinker Bell, the dandelion seed she blew in on formed her Arrival Garment.