1) Figure out the the ID of the extension. If the extension has a settings link, click it and observe the long string of characters in the address. For example, Adblock Plus has the page
chrome-extension://cfhdojbkjhnklbpkdaibdccddilifddb/options.html and consequently, its ID is
cfhdojbkjhnklbpkdaibdccddilifddb. Failing this, you can right click somewhere on the area belonging to the extension on the
chrome://extensions/ page, select inspect element—you may need to do thi twice for some reason—and look for the ID there.
2) Navigate to the folder where the extension is located. On Windows Vista and above, this is
%LOCALAPPDATA%\Google\Chrome\User Data\Default\Extensions. You should be able to copy and paste that string into the run dialog to go directly to the correct directory. Now copy the relevant directory over to the target computer, to some convenient place like the desktop.
3) On the target computer, go to
chrome://extensions/, enable developer mode and click load unpacked extension. Navigate to the folder below the first folder, showing the version number. This is the same folder that contains the manifest file,
manifest.json. There's also the option to pack an extension into a single file format that you can drag and drop onto the
chrome://extensions/ in order to install the extension on another computer.