You want to install apache tomcat with homebrew
brew install tomcat
Now go to http://plantuml.com/download and look for the section Java J2EE WAR File to download plantuml.war
Once you have installed apache tomcat copy your 'plantuml.war' into your tomcat server:
cp plantuml.war /usr/local/Cellar/tomcat/<catalina version>/libexec/webapps
You can find your catalina version under CATALINA_BASE:
catalina version
Now start your tomcat server
catalina start
In a web browser of your choice, you can navigate to localhost:8080/plantuml for your plantuml server!