The Debezium Server is a ready-to-use application that streams change events from a source database to messaging infrastructure like Amazon Kinesis or Google Cloud. To run Debezium Server with Kafka as a sink, one needs to download the Confluent Platform, compile Debezium Server, create config files, start Zookeeper and Kafka, start YugabyteDB using yugabyted, create a table and create a stream ID, start Debezium server with some configurations, start Kafka UI, insert data into the created table, and finally see the change events being populated in the Kafka topic. The setup involves several steps including downloading packages, extracting them, creating config files, starting services, and executing scripts to get the Debezium Server running with Kafka as a sink.