Very often, while observing the sky with my telescope, others ask how I find stuff so quickly without aid of a computer. I use a Meade 4.5" Newtonian. If you read ahead, I will share some of my secrets. I don't have a fancy SCT with a LX200 so I had to learn to do it the hard way. The best optical aid I've found so far is a good knowledge of the constellations. I very often don't even use my telescope or binoculars when observing. I just arm myself with a star chart and a red flashlight. I also spend a good deal of time studying / memorizing / staring at star charts. This makes for a good indoor pastime during our recent stint of cloudy nights.
Star Hopping refers to the practice of using a predetermined path of "hops" between known "landmarks" in the sky to get from an easily observed star to a more difficult or dimmer celestial object. Each successive hop is framed by stars on the edges of the field of view. Imagine using your field of view like a ruler to measure from point to point in the sky, using it to connect the dots to your target. I find it easiest to star hop with my 6x30 finderscope and then once I have found my target, center it and view it at higher power through the scope. Using the finderscope successfully requires that the scope be aligned. This is a good excuse to play with your telescope during the day. It helps to align your finderscope during the daylight hours for the first time to get a feel for how to do it in the dark. It's also easier to do the alignment on a terrestrial object that isn't moving. However, you will have to fine-tune your finderscope alignment before every observing session. Look through your main scope and find a distant point. Now find it in the finderscope, and try to center the crosshairs on the point. This procedure varies from scope to scope; on mine there are some locking screws to adjust. Loosen the locking rings and the screws. Holding the finderscope steady, tighten the screws checking the alignment in the telescope and in the finderscope from time to time. Once you're content, retighten the locking screws.
The other trick to successful star hopping is knowing exactly how big your hops are. There's an easy way and a tricky way to find out. The easy way is to find two stars that you can line up with the edges of your field of view and then check a star atlas to determine their angular separation. This works well for checking very low power eyepieces and especially finderscopes.
The tricky way to figure it out uses sidereal motion. Sidereal motion is the apparent motion of the heavens caused by the actual rotation of the earth. This apparent motion is greatest along the celestial equator. The celestial equator is the line in the sky that would be produced if the Earth's equator were projected straight out into the sky. It is here, that will get our information.
If you're not lucky enough to own a clock drive for your scope, you know first hand how frustrating sidereal motion can be. For once, here's a chance to put it to good use. While looking through the eyepiece in question, find a fairly bright star near the celestial equator, maybe something in Orion's Belt or Rasalhague, the bright star that forms Ophiuchus' right shoulder. Nudge your scope until the star is centered. Now, turn off the telescope's clock drive (if any) and time how long the star takes to drift from the center to the field's edge. This time, in seconds, divided by 120, equals the diameter of the field in degrees.
For example, if I get Deneb (alpha Cygni) centered in view in my finderscope, I find it takes 14 minutes before the star "moves" to the edge of the field of view. I multiplied 14 minutes by 60 to get 840 seconds and then divided by 120 to get a 7-degree field of view. I can double-check my math by sighting in on Phecda and Merak (the bottom two stars in the Big Dipper) and I can easily get them both in the field of view. Checking my star atlas confirms that these two stars have an angular separation of a little more than 6 degrees. Judging by the distance they appear in my finderscope, I'm fairly confident that I'm on the right track. Now that you're a pro, repeat the process through the telescope with a low power eyepiece. Find an eyepiece that gives you about one degree of field of view.
Now, for the fun. Once you have decided on a target, pick your path. You'll need two more tools. The first is a good atlas or planetarium program. I would judge this by one that shows stars to at least magnitude 6 or 7. The software is nice because you can print any amount of sky you want and to the magnitude that you need. The second tool is some rings. You need to find or make some rings that are customized to your star chart and field of view. I have some circles that I printed on a sheet of overhead transparency with a laser printer that works well with my chart. I suppose you could fashion some from a wire coat hanger. I can plot out a course through the stars with the appropriate size field of view circle on my chart. I start at a bright star near my target. This is the pivot. Moving the circle around with the edge of the circle on the star, I try to find another star in the direction of the target that will fall near the edge of the circle. That accomplished, I reproduce the view in the finderscope-first hop complete. Now slide the ring over toward the target and make the second star the pivot and set up a new view to create in the telescope. Repeat the process until I am within range of the target. (You might need to use the smaller hops provided by the small field of view of the low power eyepiece to really center in on the target. Keep in mind that when star hopping through the telescope that the field might be upside-down and backward, but the stars should all appear just like in your circle.) Having centered the finderscope on the target, the view through the telescope at this point should be very rewarding.
