It's fine to say 'I've done a training course'. This is the most natural-sounding expression for a native speaker to say. You could call the people who are being trained 'trainees', but 'participants' is the best word to use for people taking part in a course.

I can't decide. Searching on Internet I found this: http://idioms.thefreedictionary.com/take+a+course Hope it's correct!

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