How do I use JQuery to move the user's screen down to the bottom, in a very smooth way?

Suppose I have a long page of text. The user is browsing at the top.

How can I move the user all the way to the bottom of the page, in a smooth way?

.scrollto() is what you're looking for.

Here's an example of exactly what you want to accomplish.

Have you looked into scrollTo and animation?

$('html, body').animate({
    scrollTop: $("#elementID").offset().top
}, 2000);

This can be adapted to scroll to the bottom of the page.