How can I add a volume to an existing Docker container?

You can commit your existing container (that is create a new image from container’s changes) and then run it with your new mounts.

Example:

$ docker ps  -a
CONTAINER ID        IMAGE                 COMMAND                  CREATED              STATUS                          PORTS               NAMES
    5a8f89adeead        ubuntu:14.04          "/bin/bash"              About a minute ago   Exited (0) About a minute ago                       agitated_newton

$ docker commit 5a8f89adeead newimagename

$ docker run -ti -v "$PWD/somedir":/somedir newimagename /bin/bash

If it's all OK, stop your old container, and use this new one.

That´s it :)

We don't have any way to add volume in running container, but to achieve this objective you may use the below commands:

Copy files/folders between a container and the local filesystem:

docker cp [OPTIONS] CONTAINER:SRC_PATH DEST_PATH

docker cp [OPTIONS] SRC_PATH CONTAINER:DEST_PATH

For reference see:

https://docs.docker.com/engine/reference/commandline/cp/