Saliva contains opiorphin, which as an analgesic is more potent than morphine (J. Physiol. Pharmacol. 2010, 61, 483) but has a poor bioavailability (J. Physiol. Pharmacol. 2010, 61, 483; Behav. Brain Res. 2010, 213, 88). Thus saliva has some potential as an analgesic.
Step 1: Just Your Saliva
If you gather a lot of saliva inside your mouth (do not add water from outside, just secrete as much saliva as you can in your mouth) and then swish the whole saliva in your mouth - as long as you can, typically 3 to 5 minutes - the pain will subside. The saliva needs to be swallowed and replenished from time to time to ensure the levels of opiorphin, the most probable active agent.
Step 2: Just Your Tongue
If you put the tip of the tongue on the gum of the affected tooth and hold the tongue there for at least a minute - you can get some relief. Increasing the duration will definitely help. I do understand that going by the literature the saliva (or the opiorphin in the saliva) should be responsible and not the tongue, but the tongue might just be applying pressure on the nerves at that point thus numbing them until the saliva can do its job. Also I have observed that when I hold my tongue at the desired position (image), i.e. at an angle to the normal orientation of the tongue, the saliva secretion increases. Thus the tongue might be playing a dual role of numbing the nerves as well as enhancing saliva secretion.