First get a name or an ID of your docker container:
DOCKERID=$(docker ps | awk ...)
cd /var/lib/docker/aufs/mnt/$DOCKERID
Install nsenter
:
docker run -v /usr/local/bin:/target jpetazzo/nsenter
Then run:
nsenter --target $(docker inspect --format {{.State.Pid}} $DOCKERID) --mount
# create image (snapshot) from container filesystem
docker commit $DOCKERID mysnapshot
# explore this filesystem using bash (for example)
docker run -t -i mysnapshot /bin/bash
nsenter --target $(docker inspect --format {{.State.Pid}} $DOCKERID) --mount --uts --ipc --net --pid