The reciprocal melacha of mavir (igniting) is m’chabeh (extinguishing). As with all “destructive” melachos, such as erasing and demolishing, m’chabeh was done for a constructive purpose in the Mishkan: it was done to make charcoal. (This is the reason for the reference to charcoal in the chapter of Mishnayos called Bameh Madlikin, which is read on Friday nights; because making charcoal was the original purpose of m’chabeh. While both are prohibited, replicating a melacha for its original purpose is more stringent than performing an act that is essentially similar for a different reason.)
Because of m’chabeh, we may not douse or decrease a flame on Shabbos, nor may we turn off electrical appliances. It makes no difference how the fire is put out – cutting off the supply of oxygen, such as by inverting a bowl over a flame is the same as pouring water on it. If a tablecloth catches fire on Shabbos and poses no threat to human life, the proper approach is to drench the areas of the tablecloth immediately adjacent to the flame to stop the spread and quench the fire indirectly. (As with all melachos, m’chabeh is suspended when one is presented with a threat to human life.)
If a lamp is on a timer, one may not tamper with it to make it go on or off earlier, but one is permitted to adjust the dial to maintain the status quo (that is, to keep an on lamp on or an off lamp off).
This is just an introduction to the concepts of the melacha of m’chabeh; it is not a substitute for a full study of the halachos.