So you got a telescope for Christmas...

Great! So did I!

Now the sky is a big place, and telescopes don't often come with an astronomer to explain how to use them. I'm not an astronomer either, but I've been an amateur stargazer on and off for years and I might be able to give you some good advice.

First, the telescope itself. There's basically two kinds, assuming your budget was under a couple grand. There's the refractor (which has a lens on the front) and the reflector (which has a mirror at the end). If you have a cheap refractor, trade it in and get a reflector. Essentially the only parameter of interest at the amateur level is the size of the light-collecting optic, and not only do cheap lenses have poor image quality by virtue of their cheap manufacture, they are small and can't gather much light. Things will probably be dim and blurry. Now don't be too disappointed if you have a refractor, it's not a bad thing to learn with. But you want to see the wonder of the heavens and so you'll want to upgrade pretty quick. Good refractors are pretty expensive but if you have one feel free to ignore all that.

The scope I got is this beauty:

I use the stock photo because I don't actually have the scope yet. It was ordered late and so it will be here in a few days. A mere $400 for an 8 inch mirror is great. Worlds better than when I first became interested in astronomy.

So how do you find things to look at? There's two very good places to start.

First, the planets. The ones of interest are Venus, Mars, Jupiter, and Saturn. The rest are accessible with most telescopes, but you want to start with things which are both impressive and easy to find. Mars isn't actually that impressive but it's a cool pale red sphere anyway. The way to find them is fairly simple. A star chart is pretty much a map of the sky at a given time, and you can find them online for free, or in astronomy magazines. The planets are brighter than most stars, so having identified your target by your naked eye, just point the scope at it and get it lined up using the aiming reticle or little finder scope that comes with your telescope. Then using your widest angle eyepiece, find it in the telescope itself. You can then zoom in with your other eyepieces if necessary, but I encourage you to not zoom in too far as the loss of brightness and increase in fuzziness rapidly causes diminishing returns.

Second, there's the Messier objects. Way back in the day, a guy named Charles Messier was looking to discover comets. He made a list of "things which are not comets" to aid in his search. Today that list is almost universally used as a "list of awesome things to look at in telescopes". There's the Andromeda Galaxy (M31) and the Orion Nebula (M42) and the rest of the 110 Messier Objects. These are some of the most impressive things to look at in the sky. A good first might be M42, as it's easy to find in the middle of Orion's sword, high in the winter sky. "Star hopping" is the best way to find these things. Let me steal Wikipedia's description of the technique:

Star hopping uses bright stars as a guide to finding fainter objects. A knowledge of the relative positions of bright stars and target objects is essential. After planning the star hop with the aid of a star chart, the observer first locates one or more bright stars in a finderscope, reflex sight, or, at a low magnification, with the instrument to be used for observation. The instrument is then moved by one or more increments, possibly using a reticle to identify specific angular distances, to follow identified patterns of stars in the sky, until the target object is reached.

Pretty easy, all it takes is some practice. The sky isn't entirely static - the moon and planets move in regular patterns (Jupiter's moons are especially fun to watch from night to night), comets and asteroids come and go, and variable stars and novae do their own weird things. The internet is a fine and free resource, but if you have a few bucks lying around from Christmas I've always found that Sky & Telescope is pretty much indispensable. It's an excellent balance of completely practical amateur guidance alongside reports from the professional research in the field. If you just want a single book, I think Norton's Star Atlas is probably the best way to go, but you really can't go wrong with any halfway decent star charts.

Happy observing!