How to send logs to Graylog (Docker)?
Actually, it is pretty easy! Graylog's preferred Log Format - GELF - is supported by Docker natively. So if you are using Docker logs already (Docker's internal logging functionality) you can just use Docker's built-in support, that will forward all logs from your container to the specified GELF endpoint. You will have to create a GELF UDP input on the Graylog server.
https://docs.docker.com/engine/admin/logging/overview/
For running a container from command line that sends all logs to Graylog via GELF just use the options log-driver and gelf-address:
docker run -dit \--log-driver=gelf \--log-opt gelf-address=udp://192.168.0.42:12201 \alpine sh
If Graylog exposes a syslog listener you could send them with Docker syslog logging driver. But since you say you are new to Graylog, have a look at https://github.com/sematext/sematext-agent-docker which should work for you with minimal effort and will be able to also capture Docker metrics and events, not just logs, which is handy.