Let's assume we have a patient with acute infection. The doctor suspects MRSA. A culture is taken, brought to the lab, and then what?

I'm interested to hear what are the usual steps a laboratory takes to determine the bacterial species and also the subtype. Do they only rely on the way the bacteria look under microscope, do they do some kind of antibody test, or something else? Is there a standard procedure at all, or are there different methods?

Also, the test can come back as "positive", "negative" or "inconclusive" for MRSA. What makes a test "inconclusive"? Does it mean that they tried killing the culture with an antibiotic and only half of it died?