Which Docker image do you use? It will depend partly on which Docker you used, but the process is much the same.
You’ll likely need to export /var/log/suricata as a volume. For example:
docker run -v /data/suricata/logs:/var/log/suricata ...
this will make /data/suricata/logs map to /var/log/suricata inside the container, so on the host you can now see the logs at /data/suricata/logs, which you can then point Logstash, Filebeat, or whatever at to send the logs somewhere.