As I didn't find any docs for how to set up AWS S3, I'm proposing this based on stuff I pulled from various sources. Related pages:
https://doc.ez.no/display/DEVELOPER/Asset+Management
https://doc.ez.no/display/DEVELOPER/Clustering
https://doc.ez.no/display/EZP/Binary+files+handling

Clustering on Amazon AWS S3

NB: This feature is experimental, and not currently supported in eZ Platform Enterprise Edition.

Set up AWS S3 account

• Go to https://aws.amazon.com/ and create an account. An existing Amazon account can be used. http://docs.aws.amazon.com/AmazonS3/latest/gsg/SigningUpforS3.html
• Choose a region: http://docs.aws.amazon.com/storagegateway/latest/userguide/available-regions-intro.html This example is using EU (Ireland): eu-west-1
• Create a bucket in your chosen region, and make note of the bucket name: http://docs.aws.amazon.com/AmazonS3/latest/gsg/CreatingABucket.html
• Go to the "IAM Management Console" https://console.aws.amazon.com/iam/home?#/users and create a user. See http://docs.aws.amazon.com/AmazonS3/latest/dev/s3-access-control.html
• Then create a group, and assign the user to the group.
• Then assign policies to the group. The AmazonS3FullAccess policy gives read/write access to your bucket.
• Still in the IAM console, view the user you created. Click the "Security credentials" tab.
• Click "Create access key" and make note of the "Access key ID" and the "Secret access key". The secret key cannot be retrieved again after the key is created, so don't lose it. (However you can create new keys if needed.)

Set up eZ Platform for AWS S3

• In your eZ Platform root directory, run php composer.phar require league/flysystem-aws-s3-v3
• In your eZ Platform configuration, e.g. app/config/config.yml, set up the AWS S3 client:

  services:
      amazon.s3_client:
          class: Aws\S3\S3Client
          arguments:
              -
                  version: "latest"
                  region: "eu-west-1" # The region string of your chosen region
                  credentials:
                      key: "ABCDEF..." # Your AWS key ID
                      secret: "abc123..." # Your AWS secret key
  

• Still in your eZ Platform configuration, e.g. app/config/config.yml, set up the Flysystem adapter that uses the S3 client:

  oneup_flysystem:
      adapters:
          aws_s3_adapter:
              awss3v3:
                  client: amazon.s3_client
                  bucket: "my-bucket" # Your bucket name
                  prefix: "%database_name%"
  

• Still in your eZ Platform configuration, e.g. app/config/config.yml, set up the binary data handler for the S3 adapter:

  ez_io:
      binarydata_handlers:
          aws_s3:
              flysystem:
                  adapter: aws_s3_adapter
  

• In your eZ Platform system settings, e.g. app/config/ezplatform.yml, enable the binary data handler:

  ezpublish:
      system:
          default:
              io:
                  binarydata_handler: aws_s3
  

• Clear all caches and reload, and that's it.

Migrate your existing binary data to S3

Use the php app/console ezplatform:io:migrate-files command which was added in https://jira.ez.no/browse/EZP-25946, eZ Platform 1.10 and 1.7.4.