Congratulations and welcome to astronomy. Perhaps you bought a new telescope and are wondering what to buy for it in the way of accessories, Or maybe you have an older space telescope in need of telescope eyepieces. Eyepieces are the most important accessory for a telescope. Why? Inexpensive telescopes are supplied with low quality eyepieces. Upgrading to better quality eyepieces is the easiest way to improve performance. Expensive telescopes are only supplied with one eyepiece - not enough to cover all the basics. The manufacturer leaves it to you to choose more eyepieces based on your observing preferences and budget.
Matching Telescope and Eyepiece Brands
Don't limit yourself to a particular brand of eyepiece. Even if you have a Meade telescope, you can use Celestron eyepieces and visa versa. With only a rare exception, you can use any brand of eyepiece in your telescope as long as the barrel size of the eyepiece matches the barrel size of your focuser. If in doubt, measure the size of the opening in the focuser of your telescope. It will be 1" (.965"), 1.25" or 2". The 1.25" barrel size eyepiece is almost universally standard these days. A few older scopes use much inferior .965" (one inch) and a few scopes can use the larger format 2" eyepieces. If you have just purchased an astronomical telescope, odds are it uses 1.25" eyepieces. Even if it can take 2" eyepieces, it probably has an adapter that allows you to use 1.25" eyepieces.
Amount of Telescope Eyepieces
Since you will be viewing a wide variety of objects, you need to cover several magnification ranges. With telescopes, we change magnification by changing eyepieces. You will want a high magnification eyepiece for the moon and planets. You will want a medium magnification eyepiece for brighter deep-sky objects (star clusters, nebulae and galaxies) or when you need to check for more detail in these objects. You will want a low magnification eyepiece for faint deep-sky objects or very large objects. A low power eyepiece is also the eyepiece you most use for locating objects (widest field of view).
In other words, three eyepieces as a minimum. Another possibility is two eyepieces and a barlow lens. A barlow lens attaches to an eyepiece and doubles or triples the magnification of the eyepiece, depending on the magnification of the barlow. Just be sure the barlow doesn't give you too much magnification. See question six on this important topic.
Numbers on Telescope Eyepieces
That number you see on a telescope eyepiece, or listed in the description of an eyepiece, is not the magnification. It is the focal length of the eyepiece. Why not the magnification? The same eyepiece can be used in many different telescopes and can produce different magnifications, depending on the focal length of the telescope.
Letter(s) on you Telescope Eyepiece
The letter is not the brand of the eyepiece. It is an abbreviation for the eyepiece design - the combination and type of lenses used. The most common design these days is the Plossl (P). Inexpensive telescopes are often supplied with inferior designs, such as the Huygens (H), Ramsden (R) and so on. Premium eyepieces are typically labeled with the complete name.
2" yepieces vs. 1.25" Eyepieces
Two inch eyepieces exist simply because you cannot squeeze a combination of long focal lengths (low magnification) and wide fields of view in a narrow 1.25" barrel. It's a matter of lens size needed, not optical quality. You only need a 2" size eyepiece when you are exploring for low magnification eyepieces with wide fields of view. You do not need a 2" barrel on a short focal length eyepiece, even on the very finest 1.25" short focal length eyepiece. Also, before you decide to buy that premium 2" eyepiece, be sure your telescope can accept one. Not all telescopes take 2" eyepieces or offer a way to convert a focuser to 2" eyepieces.
In general, you pay more to get 1) better sharpness, not just at the center of the field, but also out to the very edge and 2) wider apparent fields of view. Telescope eyepieces that excel at both use complex lens systems of the highest quality and these do not come cheap. Using a premium eyepiece cannot always guarantee that you will see more, but using a premium eyepiece will always bring out the best in your telescope and will always make your telescope more enjoyable to use. Once you have used a premium telescope eyepiece, it is very difficult to settle for less.