"Astrophotography" aka night-sky photography, celestial photography, astronomical photography in its basic form can be and is easily done.  Don't get me wrong, photographing the night sky can be really challenging but in its basic form, anyone can accomplish it!

To start out in what we call basic camera-on-tripod astro imaging, all one needs is a sturdy tripod that when extended will reach your height.  This is important because if the tripod is not the correct height, you will find that you would need to raise the "center column" and this causes instability and turns your tripod into a mono pod.  I also highly recommend a "ball head" as opposed to a pan head mount.  The "ball head" is nice because it will allow you to angle your camera in all directions, even at the zenith.  Lastly, be sure you purchase a tripod mount that comes with a "quick-release plate".  This will allow you to swiftly mount and unmount your camera when needed for those important shots.

For a camera, it is a must that you use a 35mm DSLR and preferably a Canon.  Canon has always been the forerunner in optimizing their cameras for astrophotographers.  Nikon is also good but they are more expensive.  The 35mm DSLR will give you the most creative options, a powerful quantum-efficient sensor, low-noise and high ISO technology and so much more.  A full-frame sensor DSLR which is your equivalent to a 35mm film camera in format is the best choice.  

For lenses, optics in the range of 4mm to 55mm is best for most basic camera-on-tripod images because these lenses capture a wider angle of view of the night sky.  Just as these lenses are workhorses for your daytime landscape work, these optics are ideal for capturing a wide expense of the night sky for celestial subjects such as constellations, planetary conjunctions, meteor showers, auroras, moonlit landscapes, the milky way, star trails, etc.

Lastly, a remote shutter (electronic cable release) is the second most important tool after the tripod when it comes to camera stability and to avoid blurry images.  Since astrophotography is a unique form of imaging that involves extremely low-light and celestial objects that are light points and often very dim, it is mandatory that you keep your entire kit rock steady especially since celestial photography involves very long exposures!

So, in a nutshell, the kit you use for your daytime photography is mainly all you need for astrophotography.  This humbling and awe-inspiring astronomical photography is challenging but most rewarding.  If you are going to pursue a journey into astro imaging, start out with the most basic and easiest form -- camera-on-tripod.