Your work is stored automatically on your local computer whether you use the online or downloaded application.
For the downloaded version, your work will save to a new Twine > Stories folder in your Documents folder. As long as the files remain in this location and are not deleted, you will be able to see and open your story projects from the Story Listings view.
In the image above, you can see the Documents > Twine > Story folder created when Twine is downloaded.
For the online version, your work will save in your browser. While there are some advantages to working online, remember that if you or someone else clears your browser while you're working on your project, you could lose your work! To reduce the risk, it's good practice to "Archive" (see Twine Navigation) when you need to clear your browser, change computers, or let someone else use your computer. Archiving your stories produces a downloaded file that you can save, transport, and import to Twine if using a different computer or you lose your work.
In the side image, you can see the menu options to both Archive and Import from File located in the Story Listing view (See Twine Navigation).
When you're ready to share or submit your story, you'll need to Publish Your Story.
You can publish your story from the Story Listing view by selecting the small Gear icon for the story you want to publish (above), or from the Passages View in the Popup Title menu (below).
When you Publish Your Story, Twine creates a new story HTML file that cannot be edited. If working online, you will download and save this file. If working with the downloaded Twine app, you can save this file to any location on your computer.
To open the file and make sure it works as planned, open the file and - if prompted - select your browser of choice. Your browser should open to show the starting passage of your story and proceed as expected. If you don't see your story, try to open it in a different browser. It's good practice to test the file yourself before you send it to someone else.
You can share your story (and any accompanying media) directly using all typical file sharing methods. The file is lightweight and easily emailed alone or as a zipped drive (if you need to include embedded media). The recipient of the file will need to download the file and open it in their browser of choice like described above. Note that your story is not available on the internet at this point; you are merely sharing your work like any other type of document, with the Story file saved locally on your computer and the recipient's computer.
If you'd like to make your story public on the internet, you will need to find a site to host it. The Twine Wiki provides recommendations for free hosting options Twine authors tend to use.