The turn signal to right blinks left, and sometimes not at all on my 2005 dodge caravan. How do I determine the cause and correction of this problem?

Did this just start doing this on it's own?
The problem may be a faulty turn signal switch, or it could be that the wiring harness has become damaged.
This may require someone locally to do some close visual inspections.
Have you done any automotive electrical diagnosis before?

If no wiring has been done recently, Try your 4way flashers and walk around vehicle, see what does and doesn't work.
Try left, see what flashes and what doesn't, then right turn signals, see what flashes and what doesn't.
I agree with the Captain that it may be the Signal Head(switch).
Let us know what your results are.