Hello, I am new to Site Designer, and have a question about publishing it. I am going to publish it on another service, but can't enter the info. When I go to settings/publish, nothing can be entered in the window under "Choose where...". It shows my email under that, but when I sign out, it asks for Coffeecup login again?

Also, when I searched the Site Designer user guides with "publish", nothing came up?

To be able to publish an SD-made site, you need to use an FTP client. You can only publish to the CC S-drive directly from within SD. You can use the standalone CC app DFTP (Direct File Transfer Protocol) or Filezilla, or any other 3rd party FTP app.
You need to export the project file to get the HTML, CSS and possibly JS files, they will be sitting in a folder named 'project-name_exported' where 'project-name' is the name you have given your file.
I guess you have got the connection details from your web host, so they have to be entered into the FTP of your choice, and then you can upload everything INSIDE that project-name_exported folder, but not the folder itself.

Thanks for the info!