The hyperledger project has a built-in Docker image definition for running peer nodes. Given the vagrant focused development environment documentation, it's not immediately obvious that you can set up your own chain network using docker-compose.
To do that, first build the docker image by running this test (this test step is entirely dedicated to building the image):
go test github.com/hyperledger/fabric/core/container -run=BuildImage_Peer
Once the image is built, use docker-compose to launch the peer nodes. This folder has some pre-built YAML files for docker-compose:
Use the following command to launch 3 peers (for instance):
docker-compose -f docker-compose-3.yml up --force-recreate -d
After the container instances are up, use docker inspect to get the IP addresses and use port 5000 to call the REST APIs (refer to the documentation for REST API spec).