To play these games you have two choices.
To play offline
Download and install a Z-machine intepreter if you haven't got one already. I recommend Frotz. Then download the appropriate .z5 file and open it with your interpreter.
To play online
If clicking on the appropriate link does not start the game automatically, you will have to get it working, obviously. It runs with a Java applet. If you don't have it already, you must download the Java Virtual Machine. In fact your browser will probably tell you what you need to download.
When you open the web page in a browser (assuming Java virtual machine works), you will get a dialog saying that the applet is untrusted and asking if you want to run it anyway - click "Run".
Notes
If you've never played one of these games before, the ones I make are pretty simple. There are very few actions they even recognize, so try whatever you can think of. Just a tip, typing "z" is the same as typing "wait" and typing "x" is the same as typing "examine". You can also try "help".
Webpage maintained by C. "Sparky" Read.