There are several problems that stop us from just pointing a camera at the sky and snapping pics of distant galaxies, which need to be overcome to produce deep space photos:

• Most distant objects are very faint and very little light from them reaches us. The film or sensor in the camera needs to receive a certain amount of light to detect it, and if the object is too dim, it'll just not show up. Astrophotography uses large apertures (the opening through light enters a camera/telescope - millimeters to centimeters in a normal camera, often several meters in a telescope) and long exposures (keeping the aperture open longer, while pointing at the same thing - normal photos use a tiny fraction of a second, long exposure photos may use seconds, deep space photos may require days, weeks or months of exposure) to gather more light and make dimmer objects visible.
• Cameras and telescopes have limited resolution, which is the ability to make out small details. Achieving very high resolution requires excellent sensors, optics and a large aperture, all of which are available on high-end telescopes.
• Air distorts images and makes taking detailed pictures of the sky difficult. Astronomers overcome this either by using telescopes that are in space, outside of the atmosphere, like the Hubble, or by using advanced systems that detect fluctuations in the air and adjust the telescope to compensate (adaptive optics)

Take all of this together and it's possible to take pictures of extremely distant and dim objects.