Follow the instructions on ibm-blockchain.github.io to launch a basic IBM Blockchain network on the IBM Container Service's free plan. At the end of the install, you will be able to obtain a public URL to access your instance of Composer Playground (the UI for creating and deploying Business Networks to Fabric).
There is a single script install available as well as full documentation on individual commands for custom installations.
You will need to clone the ibm-container-service repository to get the relevant bash scripts and YAML files.