Rinne's test, often called The Rinne Test, is a simple, low-tech/low-cost test for identifying conductive hearing loss, that is, hearing loss resulting a problem in the middle ear rather than from from damage to cranial nerve VIII. While it is very simple to perform, is not a test that most audiologists will regularly use, as they have much fancier equipment that can do the same thing more much more precisely.
The test is preformed by striking a 512 Hz. tuning fork and placing the base of the fork against the mastoid process (this is the knob of bone just behind your earlobe). The sound passes through the bone directly into the cochlea, where it should be picked up by functioning nerve cells. If the patient does not hear the tone at this point, they have sensory hearing loss.
The fork is held in place until the patient can no longer hear the tone, and as soon as they indicate that they can't hear it, it is removed from the mastoid process and the fork end is held ~2.5 cm from their ear. They should be able to hear the tone again, this time through air conduction. If they cannot, you now have evidence that they have a working cochlea but not a working middle ear. Of course, at this point you don't know if the problem is an ear infection, damage to the ossicles, damage to the eardrum, or even just severe wax buildup. A visual exam will be the next step (well honestly, it was probably the previous step if your medical professional knows what she is doing) in narrowing down the cause, followed by a tympanogram.
If the patient hears both tones, this is considered a positive Rinne Test. If the patient hears only the first tone, this is a negative Rinne test. The Rinne test is most often used as part of a bedside test to determine the general outlines of a hearing problem. A negative Rinne test should result in a formal audiological evaluation at some point in the near future. It is worth noting that hearing loss at the 512 Hz. range does not necessarily indicate that a person will be hearing impaired in higher ranges (most screenings cover at least 1000, 2000, and 4000 Hz.), and that the test can be inconclusive if the patient is experiencing tinnitus.
This test is closely related to Weber's Test, which is modified to tell you which side the hearing loss is on, in addition to what type of loss it is.