Using a waterbath in baking, cooking or warming recipes consists of placing a container (for example, a pan, bowl, ramekins or soufflé dish) of a recipe or food in a large, shallow pan of warm water either in an oven or on a stovetop. The water surrounds and protects delicate foods from direct heat, allowing it to be prepared "low and slow". The French call this cooking technique au bain marie (bahn mah-ree). The name originated in the 14th century, when it denoted a utensil first used in alchemy. Of course, the name also referred to the Virgin Mary, a symbol of gentleness -- because the term implies a gentle method of cooking.

An oven or on a stovetop waterbath is typically used with delicate foods and egg-based desserts, such as custards or cheesecakes and egg-based sauces, that would curdle, break, crack or scorch under too much heat. The lower temperature prevents the egg proteins in the recipe from toughening when exposed to high temperatures. It also helps to prevent overcooking them which causes the egg proteins to overcoagulate and shrink when cooled, the classic cause of cracking in recipes! A waterbath also prevents crust formation on a custard or other egg-based dessert. With it, you also get a cheesecake recipe that is creamy almost custard-like, moist and rich. 

A stovetop waterbath is used when melting or tempering chocolate because it can burn easily from direct heat. Stirred custards are cooked in a waterbath on a stovetop, as well as delicate and egg based sauces or when heating egg whites or yolks.

NOTE: If there is some sort of starch in an egg based recipe, such as flour or cornstarch, you need not use a waterbath at all. However, some cheesecake bakers elect to use one all the time, doing no harm and providing gentle heat for a more creamy texture and a lighter color on top.   

To prepare an oven waterbath: used for baking cheesecakes, as well as other custard-based desserts, soufflés, pate or terrine. 

1. Set the oven shelf to the middle rung. Preheat the oven. Boil water for the waterbath or make sure you have plenty of hot tap water on hand.
2. You will need two pans: one that holds the recipe and the other, a larger one. The larger one should be about 2- to 3-inches wider on all sides than the recipe's pan and at least as high as the sides of the inner mold or pan; the outer pan will be filled with water that reaches about 1/2 way up the sides of the filled pan. When I bake a 9-inch cheesecake, I place it in a 12-inch round cake pan with 2- to 3-inch sides. If you don't have an outer pan big enough to hold the inner pan, use a disposable foil roasting pan. Set molds or pan in the larger pan as they are filled, leaving about 1 inch around each mold so hot water can circulate. The water should not boil around the baking pan. If it does during baking, remove some hot water with a ladle and replace with a few ice cubes.
3. If using a springform pan to bake the cheesecake in it will leak if placed in a waterbath. So, make a criss-cross of three or four pieces of foil, preferably heavy-duty, with the pan centered in the middle before filling. Bring the foil up around all of the sides to seal it and then fill the pan. But, I have found that the outside foil wrap leaks frequently letting water into the springform pan, ruining the recipe. Thus, I prefer to bake my cheesecakes in a regular cake pan where you do not need the foil because it is one piece, eliminating the seepage of water.
4. Pull out the middle shelf of the oven slightly, and place the larger pan on it. I like to put a kitchen towel right down in the bottom of the larger pan, but make sure the outer pan is high enough to accommodate both the towel and the water. The towel also prevents water from splashing in the recipe when it is poured in and hits the bottom and sides of the larger pan, plus adds some extra insulation for the cheesecake's bottom.
5. Place the cheesecake pan into the larger pan and make sure its flat. Now the cheesecake goes in the middle of that but push it over to one side just for now.
6. Carefully pour the hottest tap water or boiling water from a kettle into the outer pan. Fill the outer pan about 1/2 way up the sides of filled pan. Some recipes call for adding enough water to come about two thirds up the side of the cheesecake. Either way is fine. You don't have to go any higher than that or near the top rim of the cheesecake pan or you'll just steam the cake, which tastes horrible. You also don't want to get water or steam splashed into the cheesecake while it bakes. To prevent a skin from forming on any smooth custard, cover the mold or ramekins with foil. 
7. Carefully push the cheesecake pan to the middle and put the shelf back into the oven for baking. Replenish the water when necessary during baking ONLY if you have to. It's best to leave the cheesecake to bake without disturbing it. 
8. The important thing to remember is to remove the cheesecake IMMEDIATELY from the waterbath when done otherwise it will overbake. It will continue to bake even if the oven is turned off. Pull out the rack and gently pick up the cheesecake pan out of the water. You can remove the waterbath from the oven, but I prefer to let it cool down inside of the now turned off oven. It isn't easy to walk with a hot pan of water to the sink without dumping it down your leg. I have had that pleasure and it isn't a memorable experience.
9. To cool, and place the cheesecake on a cooling rack in a warm part of the kitchen. Handle gently as it is still quite delicate -- if you tip it or cool it at an angle, you will get a crooked cake. I like to set my cheesecake on top of a burner of the stove, because it is warm there from the heat that still radiates from the turned off oven. There it won't be subject to temperature shifts which can cause a cheessecake to crack. Don't not turn on any burners or operate the oven while the cheesecake is cooling. 
10. Let cheesecake pan cool completely. It is important to refrigerate it overnight before serving so it can firm up.

To prepare a stovetop waterbath: Used for melting or tempering chocolate, custards and other egg-based desserts.

Ramekins or tall, cylindrical pans or canisters are placed in a pan of simmering water. I often lay a folded towel on the bottom of the larger pan to keep multiple pans from rattling around, and to provide added insulation from the heat.

A Double Boiler: 

In a double boiler, the food is in a bowl suspended above a pan with and inch or so of simmering or already boiled water. It is used for food that needs gentle cooking and simultaneous whisking, stirring, or blending with other ingredients, such as melting or tempering chocolate or making stirred custards. It can also be used to keep cooked foods warm without continuing to cook them.  

A double boiler consists of two pans that fit together snugly--the top pan holds the food; the bottom holds about an inch of PREVIOUSLY boiled or simmering water; don't let the water boil while using it. You can make your own or buy one from the grocery or specialty kitchenware store.

It is very important that the hot water in the lower half of the double boiler never touches the pan above. If it does, you defeat the purpose of a double boiler; the hot water is considered to be direct, hot heat. Instead, you need a cushion of hot air between the water and the food. This helps to keep the temperature constant and the food from overheating or burning.