I know this is a bit late, but over on the Lord of the Rings portion of this site I gave an Example of Play for that game. It's not Trek, but it is the CODA system and it gives some examples that could prove helpful for you (or anyone else trying to learn the system).
Doug Taylor
Member of Decipher's Hall of Fame
Currently running The One Ring RPG. I also occasionally run Villains & Vigilantes (our campaign is in year 25) and WEG d6 Star Wars (both games are mostly on hiatus) and an annual game based on The X-Files (using Conspiracy X).