Smaller Telescopes

A telescope also needs certain features in order for it to be helpful in viewing objects.  One is it must have a well-aligned and intact mirror.  It must have at least one eyepiece, two are better.  The scope must have a mount that firm and secure.  Unstable mountings is a problem for beginner astronomers.  You should also have a finder that rides beside the main telescope.  It makes your field of view wider and makes it easier to find objects.
The first thing you should look for is the moon.  You probably won't need to use the finder as the moon is so big and bright.  However, you may need to move the telescope every few minutes to keep the moon in view due t the earth's rotation.  You should find many craters and brights spots where the sunlight covers one side of the moon.
Small telescopes are great for viewing the planets.  The rings of Saturn, the phases of Venus, and the moons of Jupiter are a few of the spectacular images you might happen across.  You must use a lower power setting because higher power makes your images dim.  Usually 80-120x is good to start out.
Deep sky objects such as nebulae, galaxies, and star clusters will be faint when compared to the planets.  The brighter the deep sky object, the better you will see it.  You can certainly observe these when you find them. 
Small telescope are inexpensive.  You can still learn a lot about them and the universe in the process.  Take yours and see what you can find in the night sky.