https://stackoverflow.com/questions/20813486/exploring-docker-containers-file-system

Method 1: snapshoting

You can evaluate container filesystem this way:

# find ID of your running container:
docker ps

# create image (snapshot) from container filesystem
docker commit 12345678904b5 mysnapshot

# explore this filesystem using bash (for example)
docker run -t -i mysnapshot /bin/bash

This way, you can evaluate filesystem of the running container in the precise time moment. Container is still running, no future changes are included.

You can later delete snapshot using (filesystem of the running container is not affected!):

docker rmi mysnapshot

Method 2: ssh

If you need continuous access, you can install sshd to your container and run the sshd daemon:

 docker run -d -p 22 mysnapshot /usr/sbin/sshd -D

 # you need to find out which port to connect:
 docker ps

This way, you can run your app using ssh (connect and execute what you want).

UPDATE - Method 3: nsenter

Use nsenter, see http://blog.docker.com/2014/06/why-you-dont-need-to-run-sshd-in-docker/

The short version is: with nsenter, you can get a shell into an existing container, even if that container doesn’t run SSH or any kind of special-purpose daemon

UPDATE - Method 4: docker exec

Docker version 1.3 (latest, you might need to use docker apt repo to install latest version as of Nov 2014) supports new command exec that behave similar to nsenter. This command can run new process in already running container (container must have PID 1 process running already). You can run /bin/bash to explore container state:

docker exec -t -i mycontainer /bin/bash

see Docker command line documentation