If you need to do this on a running container you can use docker exec (added in 1.3).

gistfile1.txt

First, find the container's name or ID:

$ docker ps
CONTAINER ID        IMAGE                        COMMAND             CREATED             STATUS              PORTS                   NAMES
b9b7400ddd8f        ubuntu:latest                "/bin/bash"         2 seconds ago       Up 2 seconds                                elated_hodgkin
In the example above we can either use b9b7400ddd8f or elated_hodgkin.

If you wanted to copy everything in /tmp/somefiles on the host to /var/www in the container:

$ cd /tmp/somefiles
$ tar -cv * | docker exec -i elated_hodgkin tar x -C /var/www
We can then exec /bin/bash in the container and verify it worked:

$ docker exec -it elated_hodgkin /bin/bash
root@b9b7400ddd8f:/# ls /var/www
file1  file2