A water bath helps the cheesecake bake evenly. Most recipes will call for the water to already be boiling before pouring it into a pan containing your cheesecake pan, but I've found that with 4" springforms, this step doesn't seem to be necessary. When making a larger cake, however, I recommend you bring the water to a boil and then pour it in once you place your pan and cheesecake into the oven.
So essentially, you wrap your cheesecake in foil and place the foil-wrapped springform into a larger pan. You place both pans in the preheated oven. You pour the water (boiling or non-boiling, depending on pan size) into the outer pan until the water comes up your springform about halfway. Bake the cheesecake.
Now, there are a couple options when removing the cheesecake from the oven. One is removing the hot cheesecake pan from its surrounding water-filled pan, and cooling it outside the oven on a rack while the water pan cools inside the oven. Another is pulling the whole thing out of the oven, which can be a little scary because it tends to be pretty heavy and easy to spill. Then you remove the cheesecake pan from the water pan and let cool on a rack.
It's up to you. But for safety, go with the first option.
