all of the previous answers are great. however if you are looking for a quick and dirty example of how to get a list of publicly available repos then check out my jsfiddle.

which uses this ajax call to list all of a users public repos:

$(#btn_get_repos).click(function() {

    $.ajax({

        type: GET,

        url: https://api.github.com/users/google/repos,

        dataType: json,

        success: function(result) {

            for(var i in result ) {

                $(#repo_list).append(

                    <li><a href=' + result[i].html_url + ' target='_blank'> +

                    result[i].name + </a></li>

                );

                console.log(i:  + i);

            }

            console.log(result);

            $(#repo_count).append(Total Repos:  + result.length);

        }

    });

});

to see what kind of data is returned just check the console after clicking the button or you can install Google Chromes JSONView extension and then just visit the url that the ajax request is making i.e. https://api.github.com/users/google/repos