To download and install Phenex, follow the instructions on the Phenoscape wiki. To launch Phenex, click (or double click, depending in your OS) the application.
When you see a message that Phenex is checking for ontology updates, the application has launched successfully. It may take a few minutes, particularly on the first run, to download ontology content.
Phenex requires Java 7 or higher. Follow this link to install the latest version of Java.