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Here are 2 methods of making pieces.  They both avoid flipping existing
pieces upside down, cutting them, etc.   The first is for long-lasting
sets (like a lifetime and longer). And the second for making a quick
inexpensive Temporary set. 

Long Lasting Method:  For permanent pieces I find Sculpy (elastic polymer)
to be great.  You can fashion a piece (as if in clay) then bake it and it
will become hard like ceramic.  You can also make molds of existing pieces
(for example: make a mold of a knight and bake the mold).  Now you can make
Sculpy Knights and modify them before baking, for instance: you can make
the Unicorn piece this way, or the Prince (cross-less King).  The Sculpy
method lets you make pieces without destroying exisiting ones.

Temporary Method: A quick and inexpensive way to make a new piece for a
variant is to make a paper pyramid of 4 sides (counting the base, which is
an equilateral triangle). Start by drawing the base on paper, then draw a
triangle out from each of the three sides of the base-- so you can cut out
the image and fold it to make a pyramid. [I also add some tabs to make the
result sturdy). Draw or paste the proper move courier image on the 3
upright faces of the pyramids. Though these 'piece pyramids' can sit
directly on a board, I cut a hole in the base and then place it over a
proper color pawn from a spare set. This gives the piece a good height. I
made these for Caissia Britannia (formerly British Chess) Lion and Dragon
pieces and it works out quite well.  Of course, I suggest this method only
for sets used temporarily, for example, if you want to have a 3D Caissia
Britannia board set up for tournament game analysis.