OnionShare is an open-source Tor-based tool for sharing files securely and anonymously.
The program requires the Tor browser to be running in the background, but otherwise there's no configuration required. Just add your target files or folders, click "Start Sharing" and OnionShield automatically sets up a temporary website to host the files (a Tor hidden service).
OnionShare provides a cryptic URL for the site, like "http://nt6ug3sqnkcd3jds.onion/kitten-table". Pass this to the recipient in a secure way, and if they enter this in the Tor browser they'll be able to download the file directly from your PC.
By default the program disables the service once the files have been downloaded once. Even if someone else finds the URL later, that means it won't be available and they'll have no way to link it to you.
OnionShare is an excellent tool which enables anonymous file sharing, without requiring any level of security or network expertise at all. Just keep in mind that Tor can be slow, and huge files may take a very long time to download.