I have done graduation caps 2 ways.
Cap base - I use the wilton mini ball pan or the wilton sports ball pan (1/2), depending on the size of the cap you want. trim a little off the back so it is flat and can better support the mortarboard. ice and cover in fondant, if desired.
Mortarboard - The first time I tried it I rolled out thick black fondant, cut a square for the mortarboard. Let dry. The other times, I have covered a cardboard square in fondant. Make sure the fondant covers enough of the bottom that you won't see cardboard when looking at the cake. I would do either way quite ahead of time. You could mix the fondant with Tylose or Gum Tex to make it dry faster/harder. Once dry, place on cap base (which should already be where you want it on the cake). You may need to use water (if fondant on fondant) or icing to help adhere it.
Tassel - I use a clay extruder and a tip that has lots of small holes. This will make lots of small snakes. Once you have it 2.5 times the length of your desired tassel, cut fondant. I take two or so of the snakes out, fold the rest in half around those two you just took out. Take a flat wide piece of fondant to wrap around all the snakes near the top to hold them all together and look like a tassel. Those two snakes that are the tassel hanger can be twisted together.
I then place the tassel on the mortarboard and arrange the tassel hanger and put a button of fondant in the center of the mortarboard.
Good luck! Here are my cakes with tassels: