What are the tests for painful joints?

Varies. X-rays are baseline, sed rate, rheumatoid factor, ANA level, lyme titer, CBC are usually performed.
Clinical eval +++. The most important 'test' is--as usual--the diagnostic tool between the physician's ears. Any well versed specialist in the field of arthritis (rheumatology) knows that hearing exactly what the details are given by the pt (history) and a careful, thorough exam of all parts of the body, will yield a dx, or at least what tests to order. Some: esr, crp, antibodies to own cells, cbc, etc.
Multiple. There are radiologic studies which can include X-ray, MRI, ct scan, arthrogram. There is blood work. The physical exam itself is a "test" that can give the examiner a good idea as to possible causes of painful joints as well.