Pretty sure you use the command wheel to change. You can "dial" faster or slower shutter speeds and the aperture will change to match (& vice versa). The camera "program" will select the correct settings for a given ISO, but you can raise or lower them a bit.
When you rotate the dial to the left or the right, this will create a different combination of aperture and shutter speed, but will give you the same brightness in the final shot. Let's say the "program" gives you f5.6 and 1/250 sec, you can rotate the command dial to achieve f2.8 and 1/1000 sec. This results in the same brightness, but different shutter speed/aperture.
For instance, in landscape photography where the camera might suggest f4 and you would rather have f16 for more depth of field. So, rotate command wheel until you see f16. Your shutter speed will change too. You're effectively doing the same thing as you would in Aperture Priority Mode. Basically, you are using Program mode to get to your preferred aperture setting. Pretty sure the D600 will "program" based on which lens you are using, as well as the light metering. EC works in this mode too.
Program tends to keep aperture open until the light gets bright enough to use smaller apertures. The exposure calculation is designed to let lots of light through the lens so your shutter speeds remain higher. This is good for hand held shots, not so much for tripod.
Used to use this early on for my D80, but switched to aperture or manual a long while ago and haven't used program on the D600 yet at all.
On the DX mode D80 my 16-85mm 3/5/4.5 VR and 70-300mm 3.5/4.5 VR had "sweet spots" around f8, so I used aperture mode a LOT.
Does anyone know if the 70-300mm retains this "sweet spot" around f8 in FX mode?