I would add the following to the points mentioned by Jamal: neuralgic pain is always unilateral and always well-localized. It is of the severe type that could be lancinating, stabbing or electric-shock like. Its duration is seconds that may rarely extend to 2 minutes. Patients may also describe a back ground pain between attacks. It does not disturb sleep. Neuralgia is usually idiopathic but it may be associated with certain diseases especially if your patient is young, say in thirties, so they should be investigated for multiple sclerosis, HIV, or brain tumor. Patients with trigeminal neuralgia may have good response to anticonvulsants particulary tegretol, phenytoin, and sodium valproate.
On the other hand, dental pain is way more common than neuralgia,so before jumping to the diagnosis of neuralgia you should examine the patient properly clinically and by radiographs to exclude any inflammatory problem in the teeth or periodontium.
Neuropathic pain (as seen in trigeminal neuralgia for instance) usually presents with a symptomatology quite different than that of "classical" odontalgia.
For instance, patients presenting neuropathic pain will usually describe it as "burning", "tingling", "electric shock -like", "pressure", "stabbing".
Furthermore, said patients will often be able to describe the pain as "atypical" (considering their past experiences with dental pain).
Finally, in some cases, successful alleviation of the pain by "neuropathic pain-specific treatments" (e.g carbamazepine, amitryptiline...) may be the only way to provide definitive diagnosis of neuropathic pain.
Unfortunately not all TN patients respond to tegretol. That is why we need sometimes to give combinations like tegretol and phenytoin or tegretol and sodium valproate . In some cases which are not responsive to medications surgery is the last resort.
I find that neuropathic pain screening tests (such as DN4) help in accurately diagnosing neuropathic pain conditions when faced with confusing orofacial pain manifestations. DN4 for instance proves to be very useful when doing a differential on the nature of the pain (inflammatory or neuropathic).
Futher information concerning DN4 can be found here:
Bouhassira D, Attal N, Alchaar H et al. Comparison of pain syndromes associated with nervous or somatic lesions and development of a new neuropathic pain diagnostic questionnaire (DN4). Pain 2005;114(1-2):29-36
Van Seventer R, Vos C, Meerding W et al. Linguistic validation of the DN4 for use in international studies. Eur J Pain 2010;14(1):58-63.