First you would look at the construction, a reflector or a refractor.
The first has at least 2 mirrors in it, and comes in several sub-types. The cheapest to begin with is a Newtonian, very cost effective. You can recognise these as having the eyepiece at the front end of the tube.http://www.365astronomy.com/images/10237-skywatcher-quattro-12s-imaging-newtonian-telescope.jpg
Newtonians however have to be optically aligned (collimated) every so often to give a sharp image. This is simple enough when you learn how, but some find it a pain.
Refractors have no mirrors, only lenses, and you can recognise these as having the eyepiece at the rear of a longish tube. They don\'t need regular collimation. The better ones have more lenses in them, and in larger sizes are very expensive.http://www.astronomyalive.com.au/media/catalog/product/cache/1/image/5e06319eda06f020e43594a9c230972d/7/0/709eq.jpg
The next spec you see is the aperture, or diameter of the optics. It is the diameter of the main mirror or lens, and governs the light gathering power of the scope. If you live in the city, there is no point to having a huge scope, as it only gathers lots of light pollution. If away from towns, a large scope will pick up faint nebula. 100 - 150mm (4"-6") is a good starter size.
Then you see the focal length (FL) quoted. This is the length of the light path in the scope. In a reflector it is folded up, and can be quite long without having a bulky tube (OTA). In a refractor it is straight, and so is limited in amateur scopes to about 1200mm.
The focal length governs the magnification you see, but only in partnership with the eyepiece (EP). These are interchangeablehttp://www.atozastro.com/my_equip/eye_pieces_set.jpg
and each has its own focal length. The magnification is the scope FL divided by the EP FL. So a 1200mm FL scope with a 25mm EP gives a magnification of x48, which does not sound much, but is good for a sweeping view of the Milky Way. EPS range down to 4mm commonly, so there is wide choice.
There is not space here to discuss the mounts, but start with a robust AltAzimuth (AZ), say a Skywatcher AZ4. Another popular mount is the Dobsonian, confined to Newtonian reflectors.
I\'d urge you not to get a cheap department store scope. These are absolute junk with plastic lenses and poor construction. Depending on budget, get an affordable refractor first up, (so you don\'t have to fiddle with it much) with some Plossl type EPs (cost effective) like a