Get an idea of where your circuit will go. You may wish to mark traces with tailor's chalk or a water-soluable embroidery marker, or just freehand it! Get your circuit board onto your taut fabric and pick up your threaded needle.
Bring the needle through the fabric from back to front, right next to the circuit board.
Pull the needle all the way through and continue pulling the thread tail until only 6 inches remains at the back of the fabric.
Leave this tail dangling for now-- we'll tie it in a knot later.
Bring your needle from front to back through the hole in the circuit board. Pull the needle and slack thread all the way through until the thread snugly hugs the conductive pad ad the edge of the board.
Repeat with a few more stitches to make a secure mechanical and electrical connection.
End with both ends at the back of the fabric and get ready to tie a knot.