On the Laravel News site they've posted a tutorial showing you how to use Minio for storage and integrate it into a Laravel application as another filesystem location.

Have you ever wanted a local version of Amazon S3 while developing Laravel applications? Well want no more, Minio is an open-source distributed object storage server built in Golang. The best part: Minio is Amazon S3 compatible. Let’s go through setting up Minio locally and then try out the new temporaryUrl method introduced in Laravel v5.4.31.

They walk you through the setup of the Minio server (locally, instructions are for brew on OS X) how to access it directly to ensure it is up and running. The tutorial then shows how to integrate it into the Laravel configuration as another file system location (as it is S3 compliant). It also shows how to create a "test" bucket for the content storage and using the "Storage" handling to push a file to the Minio service.