I am a distance runner training for a marathon. when bending yesterday, i began suffering acute lumbar facet syndrome. how long til i can run again?

Back to normal: First off, you need to get back to your normal state until you can résumé your activities (running). Otherwise, you will be prone to reinjury/recurrence of your symptoms.

Core Exercises: Typically core strengthening exercises are the best to help relieve pressure and forces in the spine. I would try and google some or look them up on youtube to see descriptions. If you can do them yourself, wonderful otherwise ask your doctor to get a referral to a good physical therapist for further assistance. Hard to say when you can start running, usually when pain has subsided.