Do you mean like a puzzle like this? Click on that and it will say that you just copy and paste in.
How to post the board on a website

What programming lanugage are you using; maybe if you intergrade the Java from chess.com to your site, it would work, maybe.

No, I mean like HTML, PHP, and those sort of things; because then you can import the games directly into the code.

There are a lot of programs that can help you create java or javascript web pages that will let you play through a game: LT-PGN-VIEWER, PGN2WEB, Chessbase Light Premium, Aquarium, Palview, etc.
I have a website and I would want to post the board with my game analysis on that website. Is this available? Thanks