Before Container Creation :
If you to explore the structure of the image that is mounted inside the container you can do
sudo docker image save image_name > image.tar
tar -xvf image.tar
This would give you the visibility of all the layers of an image and its configuration which is present in json files.
After container creation :
For this there are already lot of answers above. my preferred way to do this would be -
docker exec -t -i container /bin/bash