The Linux computers in the basement of Kemper have Java installed already. If you want to use your own computer, you'll need to install it if you don't already have it. If you aren't sure, open a command prompt and type java; a help message will print if you already have java installed. If not, go here and download the installation file for your operating system.
Download FASimulator.jar and TMSimulator.jar. The first is for both DFAs and NFAs, and the second is for single-tape Turing machines.
Once Java is installed, hopefully you can simply doubleclick on the file FASimulator.jar to run it. If that doesn't work, open a command prompt in the same directory as FASimulator.jar and type java -jar FASimulator.jar to run the program. To open a file such as a.dfa, type java -jar FASimulator.jar a.dfa; you can also open a file from within the program itself.
no-000-end.dfa and w-marker-w.tm are examples of input files to FASimulator.jar and TMSimulator.jar, respectively. .nfa files are almost the same syntax as .dfa files, except that you can write q, -> r to represent a λ-transition from state q to r, and you can write q,0 -> r,s,t to represent a nondeterministic transition to any of states r,s,t (from state q while reading a 0 ).
On Windows, if doubleclicking the jar file does not work, I found the following fix to enable it.