I own two Celestron telescopes-a 130mm Newtonian scope with a focal length of 560mm and focal ratio of f/5, and a 90mm Maksutov-Cassegrain scope with a focal length of 1250mm and a focal ratio of f/14. But what does that all mean?
When people think of telescopes, they're probably thinking of the telescope tube. This is the main part that contains the mirrors and lenses. The three main types of telescopes are refracting telescopes, reflecting telescopes, and catadioptric telescopes. This describes how the mirrors and lenses are placed, and there are many variations and hybrid designs for each type.
My 130mm Newtonian telescope is a refracting telescope, meaning the light passes through the objective (primary) lens and goes straight to the eyepiece, or to a mirror that bounces the image to the eyepiece.
My 90mm Maksutov-Cassegrain telescope is a catadioptric telescope, meaning they combine specifically shaped mirrors and lenses to form an image.
A reflecting telescope is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image.
Each type of telescope has its pros and cons. For example, I use my Newtonian scope ("Newt") for deep space viewing, while my Maksutov-Cassegrain scope ("Maks") is great for viewing inside the solar system and astrophotography. I almost always recommend refractors for newbies so they can see farther out and the planets on the way.
To change how large or small the objects appear you can use different size eyepieces, but you want to start with focal length (magnification), focal ratio (light gathering), and aperture (size of objective lens/primary mirror). The focal length determines your field of view and will impact how far you will be able to see through your telescope and aperture will determine how much light you will capture and the level of detail. The focal ratio is a unitless number, and can be found by dividing the focal length of the telescope by the aperture. For example, if a telescope had 80mm of aperture and a focal length of 500mm, then the focal ratio of the scope would be 500mm/80mm = f/6.25. That focal ratio number can really help you pick out a scope based on what you want to look at. Focal ratios of f/12 or f/20 work well for imaging solar system objects, while f/4 to f/5 focal ratios are generally best for lower power wide field observing and deep space photography.
So that's the very basics of telescopes, as complicated and confusing as it may seem. I hope this helps you pick out your first or favorite scope to get you outside and under the night sky.