In your .env file you need to set the database config values to match your database configuration. With your current settings you are trying to login to the database as the root user without a password.
You say that you're using MAMP and the default MySQL password under MAMP is root, so your .env should have these database values.
DB_HOST=localhost DB_DATABASE=laravel DB_USERNAME=root DB_PASSWORD=root
Obviously, you'll also need to make sure there is a database named laravel.
NOTE: Don't run this configuration in a production environment or any environment where security is important. It's ok for development, but for a production server I would recommend giving Laravel its own database user, and only granting that user permissions for your laravel database.