MRSA (Methicillin-resistant Staphylococcus aureus) is suspected in the face of any acute staph infection that does not respond to normal antibiotics. Even staph that is more resistant to other antibiotics than it is to methicillin is routinely called MRSA.
The standard test for MRSA (differentiated from other forms of staph) is as straightforward as it seems. After S. aureus bacteria is isolated, it is cultured in the presence of methicillin and (usually) other antibiotics. If the staph grows in the face of antibiotics that usually are effective against staph, it is obviously resistant and the diagnosis of MRSA can be made.
By using more than one antibiotic in the growth medium, the technician can identify for the practioner which antibiotics are most effective. The different antibiotics are present on specific locations on the agar (or other medium) plate, usually using Kirby-Bauer antibiotic discs . Even among strains that are called MRSA, there are variances as to what antibiotics are effective against that particular colony.
The challenging part is that the cultures can take several days, during which time the patient can be growing steadily worse. As such, sometimes it's the patient herself who becomes the most relevent growth medium.
Contamination of the medium or weak growth of the bacteria can both lead to inconclusive results.