Docker's approach to logging is that you construct your containers in such a way, so that logs are written to standard output (console/terminal).
If you already have a container which writes logs to a file, you can redirect it by creating a symbolic link:
ln -sf /dev/stdout /var/log/nginx/access.log
ln -sf /dev/stderr /var/log/nginx/error.log
After you've done that you can use various log drivers to put your logs where you need them.