for several years now, and in my experience they are the best web-hosting company I've ever encountered, and I've encountered quite a few in my time.
I must confess that I didn't know they offered free hosting packages, but anyway....
If you login to your control panel and click on File manager you'll go straight into the public_html folder, and you'll see that HeartInternet have placed an index.html file there.
The index file is a generic home page that is put there by Heart Internet, and you should be replace it with your own homepage when you've designed one. When you upload your website all the files should go into this folder, although you can create sub-directories for images, etc. Just make sure that your index file goes into the folder's root - don't put it into a sub-folder.