Like the Captain said...
Lots and lots of two-fisted action. Try to think like a Western or one of the more action-oriented war movies. This is not a period when people talk things through with the Klingons like reasonable Frenchmen () they launch into fights at the drop of a disruptor...
Scientific problems aren't defeated by technobabble either. Make sure your mcguffin (if you have one) has an obvious weakness (preferably one related to its nature), and that's the only way it can be defeated. Blowing it up in an unusual manner (i.e. not phasers or photons) is always a good way to go.
If you have the books, read the background from the Icon TOS rulebook, or (for a very nice summary) the sidebar description from the Coda book. Both give you an idea of how to proceed.
Jon
"There are worlds out there where the sky is burning, where the sea is asleep and the rivers dream; people made of smoke and cities made of song.
Somewhere there's danger, somewhere there's injustice, and somewhere else the tea is getting cold. Come on, Ace, we've got work to do."
THE DOCTOR, "Survival" (Doctor Who)