Select "special edition" from the first menu.

Highlight "play special edition".

Type in the numbers "82997" slowly. The screen should say "the future is not set".

Highlight "play extended special edition" and hit "enter".

According to THE DIGITAL BITS, the extra version adds 3 minutes to the Special Edition: one additional scene of the T-1000 searching John's bedrrom and the "Future Coda" alternate ending. I believe this is the alternate ending where we see the happy inhabitants of the future, and Linda Hamilton in some truly awful makeup.
Here is what DVD Review has to say about T2:

Terminator 2: Judgment Day
Apart from the theatrical version and the Special Edition cut of the movie, Artisan Home Entertainment's phenomenal Ultimate Edition of 'Terminator 2: Judgment Day' also contains a third cut of the film, presented as a hidden feature on the disc.
Insert the side/disc that contains the feature presentation and from the disc's main menu, select 'Special Edition' which brings up a dedicated menu to access the film's Special Edition cut. On the right hand side of the panel you will notice some weird, unreadable symbols that will give you access to the hidden feature - actually they are roman numbers.
Take your remote control and press the key combination '82997' - the date of Judgment Day in the movie - and the symbols on the side should change to the text 'The Future Is Not Set.' If they don't, please make sure to press the 'Enter' key on your remote control after every one of the digits.
Once correctly entered, the eyes of the endoskeleton will light up and you will see a new menu entry appearing, giving you access to the 'Extended Special Edition' version of the movie with the alternate ending and other scenes integrated in the film.
If this approach is too tedious for you, there's an even simpler and faster way to access the additional cut. Simply use your remote control and go directly to Title 3 and you will also get to see the Extended Special Edition cut of the movie. Please consult your player's instruction manual how to directly access titles and chapters.
But there is even more hidden material on this release. Insert the second disc/side of the DVD and bring up the main menu. Don't touch any buttons, and every 30 seconds, the disc cycles through one of three different 'breaks' - in the first the lower left hand corner flickers with lightning and the words 'Join the Resistance' appear. Select it and you will find a weblink that takes you to Artisan's website. The second break is a small head of Beethoven, which will take you to the original Swelltone trailer, and the most impressive, third break comes in the shape of the T-1000. His head will morph out of the center of the screen and says 'Get Out!' These three breaks are cycled at random. This Easter Egg is a contribution from our reader Ryan Acanfrio, Damian Murphy and John Kovach.

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