Scroll to Top Button with JQuery

Scroll to Top Button with JQuery

How can I create a button that sends a user to the top of the page? I would prefer it bring them to the top smoothly. I have a link (using <a></a>) that has the ID of #scrollUp. I also have a DIV that is at the top of the page and has the ID of #top in case I need to use it. I really could use some help with this. Many tutorials use JQuery but I can't seem to figure out how to get them to work on my website. Please help.

Is it possible for the link to be linked to the DIV that is at the top of the page but have the scrolling action be gradual? If so, I would prefer to do that.