Random quote generator from API
From spending some time looking at your code


Purely style, but I think grouping statements belonging together and commenting on them sometimes makes your code easier to read

$(document).ready(function(){
  //Take care of the initial quote
  getNewQuote();

  //Take care of click handlers
  $("#newquote").on("click", getNewQuote);//Associate getNewQuote with button
  $("#twitter-share").on("click", tweet);

  //Take care of clipboard
  new Clipboard("#copy-clipboard");
  $("#copy-clipboard").attr("data-clipboard-target", ".quote");
});

I would move the magic constants 1000 to a properly named constant
A logical OR could make this look much cleaner: ( Returns expr1 if it can be converted to true; otherwise, returns expr2. ) "" and undefined cannot be converted to true.

var author = json.quoteAuthor || "Unknown";
$(".quote-author").fadeOut(1000, function() {
  $(this).text("-- "+author);
}).fadeIn(1000);

Inside getNewQuote() I would have placed the JSON call on top of the code
You can have a list of css classes inside a jQuery call:

$("body").css("background-color", newColor);
$(".button-colored").css({"background-color": newColor,
                          "border-color": newColor});


could be

$("body, .button-colored").css("background-color", newColor);
$(".button-colored").css("border-color", newColor});


Though I do wonder how beautiful changing every single element to 1 color is, I would probably have gone with matching background, foreground, and text colors.


Other than that, this code is readable and maintainable.