It sounds like you might want to consider a basic photography class. Your question suggests your camera was previously in an automatic mode that deployed the flash whenever the camera thought it was required to provide adequate light for the exposure. If you turned to programmed exposure mode, P mode, to get the flash to stay down, that's fine but there's a tradeoff.
With no flash to provide additional lighting, something has to give. The camera typically will default to the widest available aperture and then set the shutter speed accordingly to get a proper exposure. In low-light, that means the shutter has to stay open longer if all other factors are equal. So if your flash was providing 5-stops of ambient illumination to the scene and you shoot the same scene without the flash, your shutter speed may have to go from 1/250 sec to 1/8 sec to compensate the light your flash is no longer providing.
Alternately, if your ISO setting is currently 100, you can try raising the ISO setting. In low-light, you may have to go to 800 or even 1600. There's another big trade off lurking here. Bumping up ISO may allow faster shutter speeds but, as your ISO goes up, you will start to see more noise in your images too. There's never a free lunch.
