It all depends upon who your certified through.
I believe that with IANTD you can get nitrox certified during your openwater training. Other require an Advanced card to do the nitrox class. Also, nitrox classes differ from a couple of hours of lecture to a couple of dives, and a lecture, over at least two days.
Trimix depends upon what level you want to go to. It is becoming easier all the time to become trimix trained. There was a time when you needed to be Advanced nitrox, Deco procedures, and Extended range certified before you could take the trimix class. Now, most will skip the Extended range class and have you go to mix without all of the deep air silliness.
If you have taken the GUE-F class you can go right into their recreational, no deco, trimix class- which is really a triox class since your using a 30/30 mix. This has worked out so well for them that IANTD and TDI now have recreational trimix classes in the works, some of which have been taught all summer long near my neck of the woods.
If you do the PADI, tec-rec, route you have just one class to take(tec-rec) before you can go onto their new trimix class. Of course, their tec-rec course has just as many dives in it, if not one or two more, than the standard advanced nitrox AND deco proccedures classes combined! Plus, you need to take a bunch of PADI specialties, like deep and nitrox, to even get into the tec-rec class. Maybe you can get Grant Graves to comment on it since he helped write the course and is also a member of this forum- you can also check out his Prism article.
As time goes on people are switching over to these gases with fewer and fewer dives under their belt's because they can really make your diving safer.
I hope this helps to answer your question.
Jon