Hello theRookie and welcome to CC.
There are a couple of ways of doing this. The way that's easiest for me is by ftp (file transfer protocol) which means using an ftp client software and there are many good free ones.
http://www.smartftp.com will get you one that is fine for your needs. Your internet server provider (ISP) can give you the information you'll need to log on to your server. Give their tech support number a call. You'll need the IP address, your username and password. Most ISP's have this information readily available and they will even tell you what directory to upload to. If you have this information already, create a new site in your ftp client using your server info and fire it up. In alot of cases there is a directory called 'public_html' and this is where your cart should go but your ISP can tell you what is best. Create a new folder (I call mine 'cart') and upload all the files to that folder. This way your url will be
http://www.yoursite.com/cart.
The other way is by logging on you your server's control panel via the internet. This is not as convenient in my opinion but works fine. To install the cart just follow the directions.
The installation is fairly painless if done correctly and if you need any help after uploading just give a shout and someone will help you.