home | newbie | naked eye | binoculars | telescopes | software
You'll be able to observe the moon's phases, as well as identify Jupiter, Saturn, mars, venus when they're in the nightsky. You can even watch the moon occult (go in front of) Jupiter. Depending on the darkness of your skies, you will be able to see limited messier objects like m31, m45..
I personally enjoy looking for satellites. Satellites are just any artificial/man-made objects in space. Usually, people spot them by accident as they move across the sky very smoothly (except for the fixed ones). They appear as pin points of light like stars of different magnitudes and are in view for a few minutes normally. However, you can watch out for them with the help of a great site - Heavens Above.
A note about satellites though, newbies often confuse them with aeroplanes and other stars. Aeroplanes have red flashing lights and won't visibly change altitude. Stars or planets like Jupiter could look like they're moving due to the clouds or atmosphere but satellites are distinctly moving smoothly and steadily. If you're not too sure, watch for the end when they dim out suddenly as they enter the earth's shadow. Visit the Visual Satellite Observers for more info.
Some people like to keep a logbook. It's up to you how much detail you want to note down. With practice, you'll find that you'll be able to see more with your naked eye.
Naked Eye
If you have something close to a zero budget, naked eye astronomy is for you.
Equipment
What can I see?
You'll be able to see all the bright stars easily like Sirius (Dog Star), Fomalhaut, Arcturus, Aldebaran and many more. The shapes of brighter constellations should be easy. Another fun activity is looking out for asterisms such as Orion's Belt, the Summer Triangle (Vega, Altair & Deneb), the Great Square, the Northern Cross (Cygnus) & Southern Cross (Crux) etc.