No, I've not done the journey. I just reckon that my web-searching skills are pretty good :-)
[Unlike my modesty!]
I started with the German rail website, because all European train timetables are there. That provided times and platforms but simply listed the station as 'Gen�ve'.
Then I went to the the Swiss Railways site. That confirmed the times and platforms but also simply called the station 'Gen�ve'.
I then found a map of Geneva which showed that Gen�ve-Cornavin station is by far the largest. Lastly, I did a web search for 'main railway station Geneva'. That turned up several pages which stated that Gen�ve-Cornavin station is the principal station. In particular, one organisation gave directions to their location and specifically stated that visitors should board the train to Nyon from there. I then felt confident enough to post my answer.
Now, I'll try and do my 'Sherlock Holmes' act and tell you where you're travelling to, even though you don't seem to know yourself ;-) My guess is that you're going to St Cergue. Why? Because it's the only place beginning with 'St' on a tram line from Nyon!
The timetable for the trams, including connecting trains from Geneva Airport and Gen�ve-Cornavin, is here:
http://www.tableaux-horaires.ch/bav_assets/fil es/2006/155.pdf
Chris