To put your HTML and CSS and any other files on your HostGator account, find the files on your local computer and drag them over into the /public_html folder that's already there in your HostGator files. In the FTP client, the left column shows you all the files on your own computer, the right column shows all the files on your HostGator account's server.Open up your FTP client application and connect to your HostGator FTP account: in FileZilla, you can just paste your host, username, and password into the top menu there and click the 'Quickconnect' button.Common ones are FileZilla (for Windows or Mac), CyberDuck (for Mac), etc. Once you know your FTP info, you'll need an FTP client application on your computer.
A simple way to move your files to a shared hosting service like HostGator is to use FTP (FTP stands for 'file transfer protocol').
Totally okay to have questions about this since it's your first time - there are so many things to know that aren't really talked about in 'coding tutorials'.