How would you go about coining a new word?

I’ve heard many here on Fluther say that I should coin a new word if I can’t find the word I’m looking for. How would one go about doing that? I can’t (really) just make up a new term and then stick it in my next term paper – words are only good if other people know what they mean or can find out what they mean, otherwise they loose their communication value.

Note: I’m mostly talking about non-slang words – not so much words to describe genitals or Twitter or hipster fads, but perhaps one meaning “Done in a pompously or overly solemn manner.”