Have your docker container start wait for your to enter it with the command it provides.

docker-compose-web-up.sh

# Tested on Docker 1.5
# make the following the command for docker-compose.yml
# You will obviously first need to do a chmod +x on docker-compose-web-up.sh and add it to your docker container.
# command: bash docker-compose-web-up.sh
# See https://github.com/chiedojohn/django-starter for implementation example.

# Wait a couple seconds to make sure this output is the last thing in the console
sleep 2

# Get the container ID
CONTAINER_ID="$(cat /proc/self/cgroup | grep "docker" | sed s/\\//\\n/g | tail -1)"
# Print out the command needed to enter the docker web container
printf "\nTo enter your Docker web container, run the below:\n------------\ndocker exec -it ${CONTAINER_ID} bash\n"
# The below is a hackish way to make the web container run indefinitely until stopped
tail -f /dev/null