Ah, I believe hostgator installs WP for you, so you would not have had the upload experience. I'm not familiar with hostgator, so I can only give generic instructions, hopefully that will be enough.
Log into your account control panel. Look for something like FTP or File Transfer, File Manager or similar. When you follow such a link, you should get some sort of interface from which you can move files from your local computer to your server. The INSTALL file describes everything else. You know as much as I do about the software, but I'll try to answer any specific questions you may have about it.
An alternate method, which shouldn't be required, but hosts vary on how FTP is handled, is to install an FTP client such as Filezilla on your local computer which handles moving files between local computer and server. Skip the rest of this post if you don't need or want this option.
This software will require you to enter FTP credentials in order to move files. Sometimes your account access credentials are what's needed, other times you need to add a FTP user through the host control panel to facilitate moving files. You will also need the hostname and possibly port number. The host is often just your domain, as in
example.com, but could include www, or even ftp as subdomain.
There should be a help page from hostgator with the specifics of setting up a FTP client. If no port is specified, leaving the field blank will cause the default to be used. If you do use Filezilla, it offers the ability to store your FTP password. Don't do it if you care about security. It's stored in plain text on your computer, it's safer though troublesome to enter the password each time.