The Manage Subscription Button can be configured by clicking More Views in your Customer Portal Settings. Once the additional options have been revealed, you can configure the Manage Subscription button within your customer's accounts.
If the button is not automatically displayed in your Shopify theme, it can be added in the Shopify Theme settings. Clicking Customize will open a panel to the left where you can make edits. On the website, click to log in to an account and view the account details.
From there, click Add Block. Then switch back to the Apps tab and click Manage Subscription Link. The button should now be displayed.
You can place the button in a custom area by adding the code snippet found in your Customer Portal Settings to the sections/main-account.liquid file found in your Shopify store's theme files. This can be edited from the theme settings as well.