The length of a day, or to be more precise the number of hours in a 24-hour period in which there is sun-light is a result of a relation between the earth and the sun. Daylight saving time, which is changing the official hour of the day, doesn't change the positions of the earth and the sun and therefore does not effect number of hours in which there is sun-light and doesn't, in fact, "saves" any day-light.
That, however, is not the whole story. Usually, we define the "day" as the time period in which we are awake and night as the period in which we are asleep. Note that these definitions differ from the previous ones since we (in our modern life) don't usually get up with the crack of dawn and go to sleep when the sun sets. Now, if we were to most of our activities during day-light - than we could save quite a lot of money on, for example, lighting the room.
And that is what people mean when they talk about saving day-light. There is exactly the same amount of day-light hours, but we are awake during more of them and thus saving money. Now we could do that simply by deciding to get up earlier and do all of our activities earlier. However, since that seems to confuse people (for example, we are used to have our TV programs, bank opening time and so on at a given hour), we simply move the watch instead and get the exact same effect.
As to how many day-light hour are actually "saved" (are actually been put into use by us), that depends on by how much we have moved the watch - typically, an hour.