However, enjoying astronomy is not always equal to satisfy with newly invented tools and machines, but also filled with some interest dating back to the most basic: manual star-hopping! =D
So what would you need? Simply a beginner's star charts and a decent binoculars or small telescope! For better joy, a telescope is recommended.
Once you have the atlas, the next step is to determine the visual field of the eyepiece you are using. In order to determine the power given by the eyepiece, you should divide the focal length of the instrument by that of the eyepiece. If for example we have an eyepiece with an apparent field of 50 degrees, which assembled to the telescope gives a power of 30x, then the visual field of the eyepiece will be equal to the apparent field divided by the magnifying power of the eyepiece, that is 50/30, which is about 1.7 degrees.
If you don't know the apparent field of the eyepiece the matter becomes a little more complicated... In order to find out the visual field of the eyepiece in this particular case, you should direct the instrument to a star as close as possible to the celestial equator, set the star at the edge of the visual field and measure the time it takes for the star to cross the eyepiece, without moving the instrument. Knowing that a star near the celestial equator will move one degree every four minutes, you can calculate the visual field of the eyepiece.
In order to find a celestial object with the star hopping method, the visual field of your eyepiece should be as large as possible, so don't use great magnification. This way you will be able to see several stars in the field, and will have reference points. Only when you have found the desired object should you use eyepieces with great magnifying power.
Next then to the checking on telescope.
Check the alignment of your finderscope: Find a bright star or planet, center it on the crosshairs, and make sure it is in the dead center of the 25mm eyepiece. It will be impossible to star-hop succesfully without a well-aligned finderscope. Locate the finding chart for the object you're looking for.
Center the finder on the bright, naked-eye star near the object. Knowing the field of view of your finder scope, match the stars on the finding chart with the stars you see in the finder scope. While looking through the finder scope, move the telescope so that the finder field of view moves in the direction of the object you want, but keeping some stars in the field of view so that you always know where you are. You will probably want to move only one axis at a time. You will need to move far enough that the fine-adjustment knobs won't be good enough; you'll have to unclamp the telescope and carefully move it by hand
Repeat the previous step until you get the finder scope centered on the object you are looking for. Particularly with nebulae and galaxies, you may not be able to see the object you're looking for in the finder scope! If this is the case, then you must center the crosshairs of the finderscope on the right spot so that the pattern of stars you see around the crosshairs in the finder scope match the pattern of stars you see on the finding chart.
Look in the telescope for the object. Start with the 25mm eyepiece. Focus the telescope as best you can. If you're looking for something fuzzy, you will have better luck by focusing on other stars in the field of view. If it's a double star you're looking for, you should be able to see it. If the star doesn't look double, star at it for a little bit; it may be that it's a very close double that you're having a hard time splitting! Or, you ended up on the wrong object....
If you're looking for a faint fuzzy object, like a galaxy or nebula, if you can't see it at first spend a couple of minutes looking through the telescope. Move your eye around; you may not be perfectly centered on it!You often get a better view of dim objects by using averted vision. The receptors that are most sensitive to dim light (the rods) are concentrated more away from the center of your field of vision. By looking a little off to the side of a dim object, the light from that dim object then falls on those dimmer receptors. Try this, to see if you can get a better view of a nebula, cluster, or galaxy.