This is the Docker Hub page for Ubuntu and this is how it is created. It only has (somewhat) bare minimum packages installed, thus if you need anything extra you need to install it yourself.
apt-get update && apt-get install -y iputils-ping
However usually you'd create a "Dockerfile" and build it:
mkdir ubuntu_with_ping
cat >ubuntu_with_ping/Dockerfile <<'EOF'
FROM ubuntu
RUN apt-get update && apt-get install -y iputils-ping
CMD bash
EOF
docker build -t ubuntu_with_ping ubuntu_with_ping
docker run -it ubuntu_with_ping
Please use Google to find tutorials and browse existing Dockerfiles to see how they usually do things :) For example image size should be minimized by running apt-get clean && rm -rf /var/lib/apt/lists/* after apt-get install commands.