You can upload your website files using a FTP client program. This tranfers the files from your local machine to your webspace. If you don't have a FTP program already, we suggest 'FileZilla':
Add a new site in your ftp program:
server: ftp.yourdomain.com (change to whatever your domain name is)
user: *your cpanel username*
pass: *your cpanel password*
Once connected, navigate to your public_html/ folder and upload your website files there.
If you experience connection difficulties (eg: can't get a folder listing once logged in), you might like to change the settings for that site in your FTP program to use SSL Encryption ('Explicit SSL') and reconnecting.