David Touretzky and others at CMU have written a great program called HHsim: Graphical Hodgkin-Huxley Simulator. If you want to actually tinker with the variables discussed in Chapters 1 and 2 of ICEM, it provides a great platform. It is a stand-alone implementation of the HH model of the squid giant axon (Chapter 2 of ICEM), and lets you play around with current clamp, voltage clamp, and tweak all the parameters in the HH model while seeing the results in real time. As they describe in a set of possible virtual experiments, you can also use HHsim to explore the Nernst equation as well as resting potential, so it is a useful supplement to Chapter 1 of ICEM as well. Also, installation is painless (just download the executable and double click: it will install and then you can click on the desktop icon to run it).
HHsim is educational software good for exploring some key biophysical concepts. If you actually want to construct your own models using the channels discussed in ICEM, then you will need to go to a modeling platform, most likely Genesis (their book is now available free online here), Neuron (they are finally putting out a book this year), or XPP-Aut, an underappreciated analysis tool maintained by Bard Ermentrout (book available here and helpful tutorial available here). If I have missed any software, please let me know and I'll put it in the sidebar.
Note: I am following along ICEM using Genesis, and may post some Genesis-specific posts separate from the other posts. If you are interested in doing the same, and are on a Windows machine, you should probably go through the installation hell now, as it will likely take you a few hours of labor to get it working. Once working, it is worth the initial effort.