Once you've finished your game, you probably want to let other people play it. The most important file for that is the one with the .slg file ending. That stands for "SLUDGE Game", and that file contains everything that is your game. In order to play it, the SLUDGE engine is needed, so you probably want to distribute that together with your game.
On Windows, most programs are distributed with installer/uninstaller programs. NSIS is one of the most popular systems for creating installers, and you can find a sample NSIS script for SLUDGE games on the SLUDGE site.
On Mac OS X, programs are typically contained in .app bundles. To make a bundle with your game, first rename your .slg file to Gamedata.slg, then open the engine bundle (secondary-click on the engine file in Finder, and select "Show Package Contents") and place the game file in Contents/Resources. Now the game will load automatically when you run the engine. Just zip it up (secondary click in finder - "Compress...") and send it to your players!
If you want to replace the icon shown in Finder, you can replace the file "Sludge.icns" with your own icon.
For Linux users, distributing the .slg file by itself and pointing to where SLUDGE can be downloaded should do the trick.
SLUDGE and this SLUDGE documentation are copyright Hungry Software and contributors 2000-2012