Then, from the Start menu's run line, run cmd to get a good ol' command prompt. You will need to switch to the appropriate directory with cd c:\cygwin\home\... or cd c:\temp\. In DOS-land, directories are separated by backward slashes, while in UNIX-land they're separated by forward slashes; it's just a bit of humor from the DOS people to see how often even the most experienced users screw it up. Tab-completion now works in DOS.
When you're in the right directory, just type pdrun and watch it go. Select the Prisoner's delimma game.
When you're sick of watching, go back to the DOS box and hit <ctrl>-C.
I suggest that for your first go `round, change the latticeWidth in Ascape/src/edu/brook/pd/PD2D.java, so that you can immediately see if the compilation was successful.