From very basic investigation I've come to understand that computer programs when playing humans already have openings that have been thought up by humans beforehand. So a computer may play the Sicillian Najdorf because it's been programmed to play these standard opening moves, but how would a computer play if you just gave it the rules of the game. Any examples?

Just the rules of the game? It wouldn't be able to choose moves, so I'll just assume you mean playing without any opening book.

Without its opening book, but with it's regular engine, computers usually play very logical openings. First moving a center pawn, then developing pieces. It would probably still pwn most humans.

 Cool, it's just that when I see computers play humans they tend to open with bookline variations and was wondering what they'd do on their own.

Without the demand that the program study the entire opening, a program is likely just to make some move that improves its positional score.  Center pawns that can be easily supported to gain space in the center are sort of likely, but I see a lot of initial knight moves that attack the center, flexibly.

Like dwaxe says, they will play logical moves. But there are problems: (a) obvious, logical moves are sometimes not as strong as less obvious moves developed after years of play and study by top competitors and (b) most chess engines handle some types of middlegames and endgames better than others, and an opening book can be tailored to lead to those sorts of positions. Without a book they may be led astray.

Here's a 10+5 blitz game to give you a feel for how Rybka plays without an opening book. It makes what a GM calls small inaccuracies in the opening, then destroys me in the middlegame as if I had only learned to play chess a week or two ago. ;)