How to copy files from host to Docker container

Question

I'm attempting to create a backup and restore solution for our Docker containers.

I have a Docker base image called ubuntu:base that I built and don't want to have to rebuild it every time I add files to it with a Docker file.

I'd like to write a script that starts on the host system, creates a new container using the ubuntu:base Docker image, and then moves files into it.

What is the best way for me to copy files from the host to the container?