While not strictly necessary, pins are very handy for determining the placement of your parts on your hat.
Thread two needles onto your thread, one on each end (or one at the center with the thread doubled, as shown, with the other needle threaded onto both tails).
Pierce through the sew tabs with both needles, bringing the ends to the inside and leaving a clean loop securing the part to the hat on the outside.
Tie off at each tab and snip the thread tails short.
Don't like your placement or design? No problem! Just snip the threads with scissors or a seam ripper and reposition or replace your design.