The cp command can be used to copy files.
One specific file can be copied TO the container like:
docker cp foo.txt container_id:/foo.txt
One specific file can be copied FROM the container like:
docker cp container_id:/foo.txt foo.txt
For emphasis, container_id is a container ID, not an image ID. (Use docker ps to view listing which includes container_ids.)
Multiple files contained by the folder src can be copied into the target folder using:
docker cp src/. container_id:/target
docker cp container_id:/src/. target
Reference: Docker CLI docs for cp