To simply get the value
document.getElementById("favcolor").value;
You can add an event listener if you want to get the color when the selection changes. You’d do something like this:
var theInput = document.getElementById("favcolor");
theInput.addEventListener("input", function(){
var theColor = theInput.value;
// Do something with `theColor` here.
}, false);
<input id="favcolor" type="color"/>
Here’s a working JSFiddle.