If a garment or tablecloth catches fire and there is concern for human safety, one may extinguish the fire on Shabbat. However, if there is no concern of pikuach nefesh, danger to humans, one should extinguish the fire indirectly, according to a method called gram kibui, causing the fire to be extinguished ─ but not extinguishing it directly. This is done by pouring non-flammable liquid all around the fire on parts of the tablecloth where the fire has not spread yet, but not on the fire directly. When the fire reaches the wet area, it will go out on its own. One should not use water, either due to a concern of sechita, squeezing, or since soaking a garment in water is a derivative of one of the 39 melachot prohibited on Shabbat, but one should use other non-flammable liquids. This method should be used only if one is certain that the fire can be easily extinguished within a reasonable amount of time without causing danger to anyone, G-d forbid.
Rav Yosef Yeshaya Braun, shlita, member of Beit Din of Crown Heights; One Minute Halacha, #149, reprinted from crownheightsconnect.com
