I currently have an Elasticsearch, Logstash, and Kibana all running together on seperate linux servers same network.
I wanted to add another elasticsearch to my current stack. It will be a ubuntu server.
Configure the new node to use the same cluster name (and configuration in general, although do assign a unique node name) as the existing node(s). If you're using multicast discovery that should be enough, but if you're using unicast discovery you'll have to point the new node to at least one of the existing nodes via the discovery.zen.ping.unicast.hosts option.
If you haven't already you should read the Important Configuration Changes section of the The Definitive Guide book (and adjacent sections).