Someone once said, "Only connect". And in order to connect with your audience, you first have to get their attention. Grab them by the ears, or whatever piece of anatomy is available. After that, provided what you have to offer is halfway original, well rehearsed and appealing, it is a relatively simple matter to hold them in the palm of your hand.
In rehearsal, work on your weaknesses; in performance, play to your strengths. So start with your most striking material, preferably something you can perform in your sleep (and dazzlingly when awake). If you are a brilliant guitarist, begin with a flashy display that you've been playing for years (they don't know that, do they). If you have a strong resonant voice, begin with a loud, rollicking display of vocal projection (this is usually my gambit). And if you have no great instrumental or vocal prowess, begin with something arrestingly different. As I write, two young female fiddlers have taken the stage at my local club. They are easy on the eye, which helps (and never ignore visual presentation) but they picked up their fiddles and then began vocalising, gently, in quite arresting staccato harmony - a sort of "pointillist" vocal intro - and very nicely in tune. It certainly grabbed my attention. The fiddling that followed was competent but unexceptional, but by now I was listening. With a bit more experience they will gain in confidence and "pizzazz" and will really be worth a listen. Miranda and Rachel Laurence - listen out for them in a few years.
The next rule sounds obvious but is often overlooked: always love your material. If you aren't 110% sold on it, how can you expect your audience to be? Most of us have at some time got up on stage for the buzz of performing, and forgotten that we are there to offer something to our audience; and it must be something we totally believe in, material we feel privileged to have come into contact with.
Above all, do not feel that you must present self-composed music because to do "cover versions" would be "unoriginal". The entire folk tradition is based on people doing "cover versions", sometimes of songs so old their origins are lost in the mists of time, yet some of the treatments of this material have been startlingly original - listen for instance to some of Pentangle's recordings from the '60s, Bob Fox and Stu Luckley from the '70s and '80s, or Altan from the '90s. Do not imagine that anyone is interested in your latest 10-minute outpouring of 2-chord self-indulgent drivel. Even the greatest creators of such stuff - Bob Dylan and Leonard Cohen - overdid it on occasions, and you are unlikely to have their talent.
It may be, of course, that you are a brilliant songwriter - the next Harry Chapin or Leon Rosselson. If so, you will know it. And so will your audiences. And then, milk it for all it's worth.