If a Jewish family buys a house from Gentiles, naturally the kitchen would not be left in a kosher state. What is the list of special decontamination or other upgrade procedures necessary to convert a gentile kitchen to kosher use?
This is a very fundamental question that deserves a serious answer. I am attempting to provide one based on my own experience, and my knowledge that not everyone is prepared to consult an Orthodox rabbi about this (although they really should, and it is standard for Jews to do so about such matters).
Basically, anything directly in contact with food during service or preparation needs to be formally "kashered," unless it is new. This includes appliances; dishes; utensils; surfaces (countertops, sinks, shelves or drawers) with which warm or liquid or piquant items may make contact; and all cleaning tools for the items above, such as sponges, dish brushes, and the dishwasher. Anything that cannot be kashered must be covered (preferably double-covered) with disposable material such as tinfoil or plastic for use. This is not always possible.
If the item is not new, kashered, or covered, it may not be used in a kosher kitchen. (If it is used, it may render not only the food, but also other parts of the kitchen non-kosher.) If something becomes non-kosher, it then has to be re-kashered, covered for use, or replaced with a new item.
Instructions for kashering various items can be found here. (If you learn that something "cannot be kashered," that does not mean you can just use it in its current form; it means you must either buy a new one or cover it for use.)
Once your kitchen is kosher, going forward, every dish, appliance, or surface--except those that will only be used for cold AND dry AND non-piquant items, without direct contact (such as refrigerator or pantry shelves)--must be designated for either meat or dairy. Usually, people buy dishes and utensils of two colors (often red and blue) and designate one for meat and one for dairy, or else they store everything separately, with labels. It is generally best to store meat and milk things separately (in different drawers/on different shelves) anyway.
Foods that are parve--neither meat nor dairy--may be used on or with both categories. However, a single parve item may not be "transitioned" from one category to the next. (This is an oversimplification--actually the laws on this matter are quite subtle--but don't try it unless you know them.) (Parve includes eggs and fish. Hechshers have various ways of indicating whether an item is truly parve; merely reading the ingredients list is not a reliable way to determine it.) (Some people have a third set of dishes for strictly parve food, because for complicated reasons this can be helpful at times--but it is not necessary.)
Once your kitchen is kosher (=everything listed above has been covered, kashered, or replaced with new), in order to keep it kosher, you must observe laws of kosher food preparation at all times within your kitchen. If non-kosher food (OR kosher food of the wrong category--meat versus milk) has contact with your items, the items become non-kosher and will have to be, once again, covered, kashered, or replaced. ((There are some occasions for leniency with this, especially if the contact was between two cold AND dry AND non-piquant food and surfaces, but a rabbi must be consulted.))
Non-kosher food can enter your kitchen only if it is clearly identified, separated, and double-wrapped before being placed on any kosher surface. The same applies to food of the "wrong" type (meat or milk) being placed on a surface that is designated for the other type.
The laws of kosher food preparation are extensive, but, for the purposes of keeping your kitchen kosher, they essentially boil(!) down to (1) only using ingredients with a hechsher (some products, such as fruits and vegetables, do not need to have one), and (2) keeping meat and dairy cooking completely separate. "Meat" cooking includes any cooking that has a meat ingredient, or was cooked, or includes anything cooked, on meat surfaces or dishes. This includes any kosher product labeled "meat"/"fleishig," even if it does not appear to have meat in the ingredients. (It probably means it was cooked on meat dishes.) "Dairy," similarly, includes any product labeled "dairy"/D/milk/"milchig," or that has any dairy ingredients, or that was prepared on dairy equipment, or using dairy dishes. With regards to the last point--"prepared on [meat/dairy] dishes"--this is actually a complicated issue, but to be safe, consider something that was prepared on meat dishes to be a meat product, and vice versa. For a fuller overview of kosher cooking laws, see here.
There is one more point that is not technically related to kashrus, but that is very important if the kitchen is Jewish-owned. Anything made of metal or glass in your kitchen that it is possible to remove from the kitchen must, in that case, be "toveled" before use. This means bringing it to a mikvah (a ritual pool of water intended for this purpose)--or a natural body of water that has the status of a spring--and dipping it in, often after saying a blessing. Metal and glass things that can't be removed from the kitchen have alternate procedures for tevila. (A discussion of some possibilities is here, but best to consult a rabbi.) Tevila is done after kashering (or after buying a new item) and must be completed before the item is used. Disposable items may be used, even multiple times, without tevila, if they are bought with the intention of being disposed.
If something was given to you by a Jew, or purchased from a Jewish-owned company, you probably do not need to tovel it--see here or ask a rabbi.