At the top of the list of stories, right below the language selectors is a dropdown (figure 1) where you can select 'My stories'. This will only show the stories you have selected, either by starting a story or by pinning it from the story card.
figure 1: My stories selection
Adding stories to 'My stories'
When you start a story, it is automatically added to your 'My stories' list. If you don't want to start a story yet, but want to add it to your list for future reference, you can do so by using the pin icon on the right of the story card (figure 2), next to the 'thumbs up' icon. The pin icon will turn blue to indicate it has been added to the list.
figure 2: pin a story to 'My stories'
Removing stories from 'My stories'
There are two ways to remove a story from your 'My stories' list.
The first one is available if you have selected the 'My stories' list. Here you will see a red 'x' instead of the pin icon (figure 3). Click on the 'x' and the story will be removed from your 'My stories' list. It will still show up in the 'All stories' list.
figure 3: remove a story from 'My stories'
You can also remove the story from the 'My stories' list while you're in the default 'All stories' list by clicking on the blue pin icon. The pin icon will then turn grey to indicate it has been removed from the 'My stories' list.