As to where to put it, you just put it into the box provided for your CSS additions to your site. Go to Dashboard > Appearance > Custom Design
On this screen, choose the CSS and you will be taken to the area where you can add your CSS. You don't copy the existing CSS sheet in, you just put your changes in the box provided. Just copy what you have here and add it in at the bottom of any other CSS that you have added. Save it, and check out your site to see if it did what you wanted done.

For a more thorough explanation see the support document:
http://en.support.wordpress.com/custom-design/#custom-css

Done a bunch of reading about how to change this but I'm not sure where the information needs to go in the CSS in order to hide the Category Archive.

Saw someone posted that you need to put this into the CSS:
.archive .page-title {
visibility: hidden;
}

.archive .page-title span {
visibility: visible;
float: left;
}

But where does that go? Would love some help... thx