The test takes advantage of the fact that pre-renal causes of ARF are all due to renal hypoperfusion. The kidneys take this to imply (usually accurately) that the systemic blood pressure is low, and so they start shutting down to avoid you losing too much water courtesy of your urine. Also, in prerenal dysfunction, the renal tubules are intact, and they reabsorb as much filtered sodium as possible - sodium is highly osmotically active, and so this is one method of reabsorbing as much filtered water as possible.
On the other hand, the vast majority of intra-renal causes of ARF are due to acute tubular necrosis, where insults such as hypoperfusion and toxins cause the tubular cells to die. When this happens, the tubules will be unable to reabsorb the sodium appropriately.
So, the fractional excretion of sodium basically looks at what proportion of the plasma sodium finds itself in the urine. With pre-renal dysfunction, this figure will be low (most of the sodium is reabsorbed long before it gets to your bladder), whereas in acute tubular necrosis, the figure will be higher (less sodium reabsorption).
A clear consensus for normal values is sorely lacking, but most people agree that a fractional excretion of sodium (FENa) of > 3 indicates ATN.
The FENa can be calculated by the following formula:
(FENa) = (UNa x PCr) / (PNa x UCr) x 100
(where U stands for urinary and P stands for plasma)