There are three steps to kashering a microwave oven: 1) cleaning it thoroughly of any residual food resulting from spillage or steaming; 2) heating a bowl of water for about ten minutes at the highest setting – to kasher it from ḥametz steam and vapor using the principle of ke-bole’o kakh polto; 3) since there is concern ḥametz may have spilled onto the plate that sits on the microwave’s turntable, one must clean the plate and perform hagala on it with boiling water, or, alternatively, place something as a barrier between it and the food that will be heated in the microwave on Pesaḥ.
Dishwashers: The filter, where residual food often gets stuck, must be cleaned thoroughly. Then the dishwasher should be run, with its racks, at its hottest setting, so that any absorbed ḥametz is released, ke-bole’o kakh polto.
. Some are stringent and consider dishwashers to have the status of a kli rishon on a flame. This means that to kasher a dishwasher one must put a white-hot piece of metal in it in order to bring the water to a boil. However, those who follow the lenient approach have authorities on whom to rely. Others are stringent about this because they have a custom, le-khatḥila, to kasher everything in a kli rishon on the fire. So state Igrot Moshe, OḤ 3:58, and Sidur Pesaḥ Ke-hilkhato 8:32. However, in practice, a dishwasher should not be considered a kli rishon, because only where the water is heated up is considered a kli rishon. However, from there the water is injected into the hollow center of the dishwasher, and when the water arrives there it has the status of something poured from a kli rishon – and ke-bole’o kakh polto. Regarding what Rema writes, that there is a custom to kasher everything in a kli rishon, this is only le-khatḥila, and even then, it is only due to the concern that the kli may have been used in a more intense fashion. In the case of a dishwasher, there is no such concern; this is the accepted ruling (Hagalat Kelim 13:225-227; Or Le-Tziyon 3:10:11 states that technically it is permissible to kasher just by cleaning). See Peninei Halakha: Kashrut 25:8, n. 10.