How to relieve pain in lower back due to facet joint problems?

Several ways. We start with anti-inflammatory medications, pain medication, if did not help we move to steroids by mouth or injection under fluoroscopy and the last resort is surgery.
Facet Treatments. May help depending on your pain issue. Facet injections are helpful and can be long-lasting, however if your get short lived relief you may need to get evaluated for a radiofrequency ablation for longer lasting relief (greater than 1 year of relief is typical).
Facet Follies. Facet arthropathy, or vertebral arthritis, is a challenging condition to manage, but not impossible. Relief comes primarily with strengthening the supporting structures around these joints. In doing so you can relieve positional pain. The difficulty with complete relief is due to the fact the spine is mobile. Fusion of involved vertebra also helps, but stresses the joints above/below the area.
Multiple options . Many treatment options for facet issues. Medications, physical therapy, chiropractic care, facet joint injections under fluoroscopic guidance and acupuncture are some options. Candidly, it's not easy for physicians to reliably predict what patients will favorably respond to which of these options.