You will need:
base color - clear top coat - small feathers - small pair of scissors
Start by applying your base color.
Now you can select and arrange your feathers.
Apply a clear top coat nail polish and carefully place the feather on your nail. Push the feather gently in place.
When dry apply a top coat 2x and trim the edges with some small scissors.
You're done. I've chosen to take a bit off each side of the feathers to create small feather flames on the nails.