One thing that is often overlooked with any new telescope is aligning the small sighting "finderscope" with the "big" telescope. In the daytime, find a distant stationary object like a telephone pole. Sight along the telescope tube until you locate the pole and crossbar in the center of the eyepiece. Now adjust the finderscope (using the adjustment screws) until it too has the pole centred. It has a pair of "crosshairs" like a rifle scope that makes this easier. If there are no adjustment screws, try placing a few thicknesses of paper under the bracket which holds it until both telescope and finderscope are aligned with each other. Be sure all the screws are snug, but don't get carried away. Read more
It has been said that beginner telescope observers often look only for 15 seconds, on average, at an object. And of all the objects in the sky only Jupiter, Saturn, the Orion nebula, the Pleiades and the Moon (for N. hemispherians) are the main targets (mostly by being bright and easily findable). The low-down is that 15 seconds is not enough time to really SEE the object.
A few small easily remembered tips will improve your observing skill.
First, and most importantly, dark adapt your eyes. Set up your telescope away from direct lights. Urban observers may have to resort to using light shields (a wind break can be used) to shade their eyes and scope. The site should be away from all convecting heat sources. A field is ideal. Observing through open windows, on the top of a building or on a concrete/tarmac surface is not recommended as these will cause a lot of atmospheric distortion and loss of detail*.
Once dark adapted and comfortable, remember to relax your eyes. A hand or pirate eyepatch over one eye may help when looking through the eyepiece.
Once you have found your target object occasionally look indirectly at it. Using averted vision will help spot faint objects. And strangely, tapping the scope and making the object dance about can also help identify subtle features.
*Even in seemingly ideal conditions the atmosphere is constantly distorting the image. But occasional there is a 'window' through that distortion... when everything is clear and still for a moment. The trick is to learn to have have a 'photographic memory' of when the seeing is clearest. Observing the object with a few of these 'moments of clarity' will help confirm very subtle detail.
Remember to breath.
Use a logbook, or sketch what you see. A voice recorder could also be used. Likewise, a webcam can help improve object observing time... and help identify unknown features. A logbook can help with future observing sessions and help to plan for future target objects.
The longer you look at an object the less likely you are to miss something.