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Turbos work from exhaust pressure. At extremely low RPM's (idle), the turbo is spinning, but not fast enough to create boost. As RPM's come up (as low as 1200 RPM on the TDI), boost is delivered and power increases.

There is no sleep mode for your turbo. If your engine is running, the turbo is spinning.

Here are a couple of links that do a good job of explaining how they work. Check out the first video - it's the easiest to understand.

Cummins Turbo Technologies -> Products & Technologies -> Turbocharging Explained -> How a Turbocharger Works
How Turbos and Superchargers Work - Engine Intel - Popular Mechanics