Draw a beard shape on the back of the faux fur with your Sharpie. You can use the template I've provided.
Cut the faux fur piece out with scissors. Pull the fur/beard material forward AWAY from you while cutting, towards the front of the fur. This is so you only cut the background of the material, rather than snipping random fur pieces off.
Place a line of hot glue across the top of the beard and attach to the circle a little under halfway down. Let cool.
Draw a triangle with a base slightly larger than the wood circle onto the felt with Sharpie (about 2.75" base).
Cut the triangle out with scissors. Then use that hat as a template to cut one more out of felt.
Glue the triangles together by placing a line of hot glue on the long sides and smoothing together. Let cool.
Turn the hat inside out and set aside. It should fit over the circle, but if it doesn't, you can stretch it a little.
Place a dab of hot glue onto the wood ball and attach as a nose.
Drill a small hole into the top of the wood circle. Tie a 12" length of baker's twine into a knot at one end and pull through from front to back.
Cut the very tip off the top of the gnome hat and thread down onto the baker's twine and onto the head.
Organize the hat so the seams are on the sides and glue down around the ornament onto the nose to finish.