How to Buy a Telescope on eBay

This guide is aimed at the beginner who is looking to buy his or her first telescope. I'm assuming you know little about telescopes. My mission is to give you as much information as I can as quickly as I can so I'll be revising and adding information as I have the opportunity to edit it. Let's get started.
There are two kinds of telescopes: refractors and reflectors. Both come in a number of variations, some of which are quite exotic and expensive.
All telescopes have three key components that each have a key measurement: The objective (and its aperture), the tube (and its focal length) and the eyepiece (and its focal length).
There are two other important components: The finder scope is a smaller (but wider view) scope attached to the main tube to help in initially locating objects. Astronomical scopes require a mount, which is usually connected to a tripod, although spotting scopes and monoculars are frequently handheld. An astronomical telescope without a mount (but sometimes with an eyepiece and/or finder scope attached) is called an optical tube assembly (OTA).
The aperture (size) of the OBJECTIVE determines the light gathering power of the telescope. The objective is the big lens on the front end of a refractor and the big mirror at the back end of a reflector.
A REFRACTOR is the "classic" design that probably comes to your mind when you hear the word "telescope". Big lens on one end, (the objective) and a little lens at the other end. This little lens is the eyepiece through which you view what you're looking at. This is the design that is said to have been invented by Gallileo.
In the past I've said to "Forget about refractors." That's because it's surprisingly difficult and expensive to make a quality refractor. The problem is that the way refractor obectives bend light causes the different wavelengths (i.e., colors) to bend at different angles. This causes a problem called "coma", which is a rainbow aura around objects like stars and planets. Achromat refractors use a second lens to partially correct the coma problem, adding to the cost. The apochromat refractor adds yet another corrective lens at even greater expense. However, if you're particularly interested in viewing the moon and planets (for which refractors excel) as opposed to deep space objects and you have a generous budget, a refractor might be your best choice.
I still believe, however, that a REFLECTOR is the best type of scope for most beginners. The objective in a Newtonian (as in Isaac) relector, the simplest kind, is a mirror at the bottom of a big tube, whose front end is open. The mirror is curved and refects the image back into a secondary mirror suspended near the top of the tube. The secondary mirror reflects the image into an eyepiece that sticks out perpendicular from the main tube near the top of the tube. Yes, the secondary is an obstruction but you don't actually see its silhouette when you look through the eyepiece. It merely dims the overall view.
Here are some quick facts:
Magnification is determined by dividing the focal length of the main tube by the focal length of the eyepiece. (Any good ad will give you the focal length of the tube and any eyepieces included.) For example: A scope has a focal length of 1,000 mm (1 meter, about 39 inches). If you drop in a 25mm eyepiece, magnification will be 40x (1,000 / 25 = 40). Drop in a 10mm eyepiece and magnification will be 100x. You can always buy more eyepieces.
So if magnification is dependent on focal length, what does increased aperture get you? Compare a 4" aperture scope with an 8" aperture scope. If they both have a 1,000 mm focal length with 20 mm eyepieces, they'll both magnify the image by 50 times. However, the 8" scope, with twice the diameter of the 4" scope will give you an image four times brighter. Light gathering ability increases by the square of the radius. Objects that are barely visible in a four inch scope will be quite bright in an eight inch scope. By tradition, the aperture of some kinds of scopes is given in inches while others are measured in millimeters. (One inch = 25.4 mm).
Most scopes use standard 1.25" (width) eyepieces. Different brands and designs can be used interchangeably. Some scopes use 2" eyepieces. These usually have adapters so they can also use 1.25" eyepieces. (Another, less common size is 0.96 inches.)
Despite the outlandish promises that may appear on a scope's box (such outlandish promises being a good indicator that the scope is junk) the maximum usable magnification is about 50x the aperture measured in inches or twice the aperture measured in millimeters. For example, a 5" scope is good for a maximum of about 250x. A 90 mm scope is good for about 180x.
Maximum magnification does not always provide the best view. For a given aperture you can't magically increase the amount of light the scope gathers. What does this mean? The greater the magnification you use, the dimmer the view will be. Think about it: If you take the same amount of light and use it to make a bigger image, the image has to get dimmer.
Forget about seeing views like the gorgeous photos that illustrate the boxes of some scopes. They're generally taken by giant scopes and they're made up by overlaying dozens, sometimes hundreds of repeated exposures. And each exposure may have lasted many minutes or even hours. Remember learning about the rods and cones in your eyes in junior high school science? The rods, being much more numerous and more sensitive to light, provide most of your night vision. But they're much less sensitive to color than the cones are. So the images you will see will be pale with only a hint of color.
If you can't afford to spend at least $200 on a scope consider buying a good pair of 10 x 50 binoculars for as little as half that. (The "10" refers to the magnification, which is usually fixed in binoculars; the "50" refers to the size of the objectives, 50mm.) There are whole books written on naked eye and binocular star gazing and binoculars are a great way to get into the hobby. As a bonus if the interest in astronomy wanes the binos will still be good for hiking, camping, bird watching and so on