It looks like you've not attached a screenshot to your post so I'm not able to take a look at your Filezilla window.
At its most basic, all you need to do to have a gallery live on your web server is upload the entire gallery folder to your web server (anywhere will do as long as you know where it is).
You can then view the gallery (on its own web page) by visiting the gallery's 'index.html' file (inside the gallery folder) in your browser.
I'd recommend uploading the gallery to the root directory of your web space for convenience.
The root directory is the directory that you'd upload a file (or folder) to so that it is the first thing in the URL after your domain name.
For example, if you uploaded a file named 'test.html' to your root directory and your domain name is www.example.com, then you would be able to view the 'test.html' file using this URL: http://www.example.com/test.html.
The root directory is usually named something like 'public_html', 'htdocs' or 'www' but if you are unsure what your own root directory is named (or how to navigate to it using an FTP program), then your web host should be able to help you out.
Once you've got the gallery uploaded to your web server, you can then embed the gallery into an existing web page alongside other content (if you want to), by copying and pasting the embedding code I posted above into your web page wherever you want the gallery to appear. (The embedding code assumes that your gallery folder is named "my_gallery_folder" and has been uploaded to your root directory. As long as this is true, then the embedding code can be used exactly as it is without modification.)
I hope this makes sense.
If you continue to experience difficulties, then please let me know how far into the process you get and what seems to be the stumbling block.
Also, please post the screenshot you mentioned so that I can see what you are referring to. It might help me to troubleshoot your problem. Thank you.