First of all, it depends on how long have you been fingerboarding before. The longer, the more rapidly you'll be ready for session. You'll warm up sooner.
Anyway, you have to go from a general warm up, aimed at increasing general blood flow, heart rate, etc; to a semi specific one, aimed at recruiting blood to the area that will be targeted by the excercise (shoulders, arms and fingers in your case); to a specific one, in which you mimic the very same excercise that you're going to perform, same movement patterns, etc, only at a lower intensity.
Then, after the complete warm up, you'll start from the hardest hangs, always leading with the weaker arm if you're doing one armed hangs.
Hope this helps.
Warning: if you've never fingerboarded before, you can still avoid it. If you're already hooked, oh well, welcome to the dark side of climbing.
