There are many ways to do it. First, go to your profile and then tap the 'Archive' button. As mentioned above, you will see all stories you have shared on your Instagram Stories. Choose the story you want to save, and tap on it. You will see the download arrow at the top of the page to save the story on your phone. Secondly, you can take a screenshot. To do that, if your device is iPhone, press the volume-up button and the side button at the same time. On the other side, if your mobile device is Android, press the Power simultaneously and press the volume-down button.