I have my Intel Galileo setup as a Morse Code device. The user can press a button to send a "." to the LCD screen or press and hold the button to send a "_" to the screen. The program then decodes the Morse Code to the proper alphanumerical representation of the morse code. I now want to set up my board as a server that sends this data to be displayed on web page. This brings me to a few questions, how do I send info to such a web page and how do I create such a web page?
how do I send info to such a web page
You don't. You send a web page, if you are are server, and the client (browser) asks for one.
Or, you act as a client, and make a GET request, to a server, and have the server do something with the data. The browser, as another client, makes a GET request, to the same server, to get the new data. It has NO way of knowing that there IS new data, so it shouldn't ask too often.
how do I create such a web page?
With a text editor, of course.