Using the LinKnot package
The Mathematica package LinKnot is a combination of two packages. The first, "Knot2000" was written by M.Ochiai and N.Imafuji. This was extended to the package "LinKnot" by S. Jablan and R. Sazdanovic. This package provides many useful things KnotTheory can't do natively; for example, it can interpret Conway notations, and, at least on Windows machines, provides nice graphics for knots, and a graphical interface for drawing knots by hand.
To use LinKnot with KnotTheory, you should download LinKnot, available from [1]. Install this wherever you like, and in your Mathematica session issue a command like
After you've done this, everything should just work. (LinKnots` will only be loaded when necessary, and there might be a short delay when this happens.) If everything doesn't just work, please complain to Scott.