How would I go about starting an application in my host machine in order to read files and stdout from a running docker container?
Essentially I want to do this:
The stdout of the process started by the docker container is available through the docker logs $containerid command (use -f to keep it going forever). Another option would be to stream the logs directly through the docker remote API.
For accessing log files (only if you must, consider logging to stdout or other standard solution like syslogd) your only real-time option is to configure a volume (like Marcus Hughes suggests) so the logs are stored outside the container and available for processing from the host or another container.
If you do not need real-time access to the logs, you can export the files (in tar format) with docker export