If someone is going abroad and thus leaving their house for Pesach (to avoid all doubt, leaving their house before Pesach, and arriving back after Pesach), than what cleaning and preparations must they do in their house before they leave?

Shalom, According to the standard laws, if someone is leaving their house and it will not be used during Pesach, one is still obligated to remove all chametz, though there is no need to "kosher" the kitchen. In practical terms this means you must go through the house to check for any chametz and remove it as you do every year. In the kitchen, all chametz must also be removed and you need to clean well to make certain that no chametz remains - for example, inside the oven, remove any visible crumbs, and check behind the fridge for fallen chametz. But you do not need to "kosher" the oven, stove-top or surfaces for Pesach as you would every year, it is enough just to clean them from all visible chametz. If you have chametz of value left over that you would normally sell, such as whiskey, it should be all be placed together in one cupboard or room (such as the kitchen) and the regular sale of chametz should be done through your local Rabbi. On the night before you leave, you should do a "bedikat chametz" (search for chametz) with a candle like every year, but without the blessing. However, many people find checking the whole house very difficult, and if there is good reason, one may exempt themselves from this by selling all the chametz in the house to a non-Jew. This exempts the house from the need to do a bedikah (check) and from getting rid of one's chametz. Some people use a special form of chametz selling that has the sale take effect one day earlier than usual, so that the house is not under your ownership on the night of the checking. This is a stricture, but even the normal chametz sale (which takes effect on the morning before seder night) exempts one from checking at all according to most opinions, and one may rely on it. If you choose to do this, you do not have to do a check of your house, or remove anything, it is enough just to close up the house and rely on the sale (it would be advisable to leave a key with a neighbor so the non-Jew can get to his chametz if needs be). In any event, you should do a bedikat chametz (check for chametz) in the place you will staying for Pesach (or at least help your hosts do so), and say the "bitul" (nullification) as you do every year on the night before Pesach and in the following morning. Blessings.