1. You should have a story file with an extension like .zblorb or .gblorb or .z5 or even .z8
2. Download an interpreter:
Zoom for Mac OS X, maintained by Andrew Hunter.
Zoom for Unix or Linux, maintained by Andrew Hunter.
Spatterlight for Mac OS X, maintained by Tor Andersson.
Windows Frotz, maintained by David Kinder.
Windows Glulxe or Git, maintained by David Kinder.
Gargoyle for Windows, maintained by Ben Cressey.
iPhone Frotz, maintained by Craig Smith; a free app at the iTunes Music Store, for use with the iPhone and iPod Touch. (This comes with a nice collection of Z-machine story files already built in, but - being basically Frotz - won't play Glulx titles.)
3. Open up your story file in the interpreter!
4. Marinate in your newfound ocean of narrative.