What sort of test do they do for someone with arthritis?

See below. If the arthritis is confined to a single joint, maybe only an xray. If there is arthritis in multiple joints on both sides of the body, certain blood tests may be run looking for rheumatoid arthritis or similar conditions. These include, rheumatoid factor, antinuclear antibody, anti ccp antibody, sedimentation rate, c reactive protein, uric acid levels among others.
Many types. It depends on what the history and physical shows. We have a variety of lab tests, imaging including x-ray that we use.