Other than the obvious answer - Know stuff, help people, be nice - How does a forum user get a Community Expert medal?

I believe this is automatic; it started when IPS was updated to v5, from Gemini:

In Invision Community 5 (New Feature)

Version 5 introduces a native, automated Community Experts system. It is designed to automatically identify and label helpful users without constant manual intervention.

• How it works: The system uses an algorithm to identify experts based on their helpfulness in specific forum sections.

• The Metrics: It looks at data points such as:

  • The number of "Solved" answers they have provided.

  • The volume of "Helpful" votes (reputation) on their replies.

  • The speed of their answers.