The Halachot of using ovens and microwaves span both year round and Pesah.
It is clearly prohibited to cook meat and milk simultaneously in a conventional oven. The Poskim discuss whether one may cook meat and milk consecutively, e.g. a meat dish today and a milk dish tomorrow. The issues is that the vapors from the meat dish are absorbed in the walls of the oven and will be released when cooking the milk dish. Following the principle of "K’bol’o Kach Polto"(the way in which it was absorbed is the way in which it is released), the only way to purge the meat from the oven is fire. Since it was absorbed through heat, it will be released by heat. Using a blowtorch on the walls of the oven would effectively neutralize any meat essence, but it is not feasible, since it may ruin the oven. Hacham Ovadia rules that it is sufficient to wait 24 hours in between the use of meat and milk and then burn out the oven by turning it on to a high temperature, while empty, for 15 minutes. If there are any drips or spills of food substance on the walls, they must be cleaned off. That combination of waiting and burning resets the status of the oven.
This method of Koshering as known as "Libun Kal"-a minor burning out, which could ignite a piece of straw. Hacham Ovadia rules that it is sufficient here, even though Maran generally holds that a more intense burning, which emits sparks, is required. This leniency is based on several factors. First, the oven absorbed kosher food, "Hetera Balah"; i.e. the meat or dairy that was absorbed is only a problem when mixed together, but there is nothing intrinsically wrong with it. Furthermore, the meat that was absorbed is not the actual substance of the food, but merely the vapor. Of course, a self-cleaning oven is considered an even more intense method of purging the oven.
According to this, if a woman cooked an uncovered dairy dish on Thursday night, she may not use the oven the next day to cook meat for Shabbat, because 24 hours have not elapsed. Therefore, one should pay attention to the time of cooking dairy on Thursdays. However, if the first dish is covered with aluminum foil, there is no issue of the vapors.
Hacham Ovadia’s approach is also lenient in respect to switching freely between milk and meat. This is in accordance with the Hida and the Peri Hadash who permit it, and disagree with the strict position of the Magen Abraham who was concerned that one may lose track of the status of the vessel.
The question of using a microwave oven for meat and milk is contingent on whether its walls get hot. There seems to be a difference of opinion between the technicians on this matter. Hacham Ovadia concludes that to make a microwave Kosher for Pesah, one should boil soapy water for 15 minutes and the vapors will extract any Hames absorbed in the walls. He presents a lengthy discussion with proofs from the Maran and the Peri Megadim that vapors have the ability to extract.
Regarding year-round use, one should always cover each dish he heats up with the special microwave plate cover. He should have three covers: Meat, dairy and Parve dishes. That way any vapors that escape the food are absorbed in the cover and not in the walls. If one heated up a food, e.g. pizza, without a cover, the microwave becomes dairy and may not be used for meat until it is koshered by boiling soapy water for 10 minutes inside of it. This is the conclusive practical Halacha, even though there were some Poskim who had a more lenient approach. This is also the method to kosher microwaves commonly found in hotel rooms: The microwave should be cleaned, the soapy water should be boiled, and then the kosher food may be heated using a plate cover (to be on the safe side).
All of this assumes that a person has only one oven. If a person can have two separate ovens, that solves all the problems and is much easier. However, the Halacha does not require a person to own two ovens.
In order to use an oven for meat and milk consecutively, it must be totally clean of any drips or spills and then wait 24 hours and burn it empty on a high temperature for 15 minutes.
A microwave must also be koshered between meat and dairy by boiling soapy water in it for 10 minutes.
If the first dish was covered, there is no need to kosher the oven before cooking the next dish.