First of all lets look at the writing found around the barrel of the lens.
Next to the Nikon name is usually something like DX or N.
DX means it is a lens designed to be used on DX format APS_C cropped sensor cameras rather than full-format FX cameras.
N means the leans is treated with a nano crystal (anti-reflective) coating.
Below the name is some writing.
Example AF-S NIKKOR 55-300mm 1:4.5-5.6 GED
AF-S simply means it is an autofocus (AF) lens rather than a manual focus one. And the -S means it is a silent wave motor ( a quiet one with fast autofocus)
NIKKOR means the lens is made by Nikon
55-300mm is the focal length of the lens. Because there are two numbers 55 and 300 this lens is a zoom lens with a range from 55mm up to 300mm. If there was just one number, e.g. 85mm then the lens would be a prime lens, i.e. one with a fixed focal length.
14.5-5.6 indicates the maximum aperture. Because this is a consumer telephoto, the maximum aperture varies across the zoom range. At 55mm the maximum aperture is f4.6 but this decreases to f5.6 at the 300mm end of the zoom range. Some zoom lenses and all prime lenses have only one number e.g. 1:2.8 This means that the aperture is fixed (f2.8 in this example) across the entire focal length of the lens. Zoom lenses of this type tend to be more expensive. Note: the smaller the number, the greater the light gathering power of the lens and the better it should perform in low light conditions.
G means that this Nikon lens is "gelded" , i.e. it does not have an manually adjustable aperture ring which was common on older manual lenses. G II means it is a second generation lens for this focal length featuring VRII technology.
ED means that the lens contains Extra low-Dispersion glass that helps correct chromatic aberrations (failure to focus different colours at the same focus point)
Below this writing a couple of letters may be found , eg. VR. This stands for Vibration Reduction or image stabilization. This is a feature built in to the lens to reduce blur when hand holding a lens. Not all Nikon lenses will have this feature. Other manufacturers call this feature something like IS, OS, or VC
Finally, if you remove the lens cap and look at the inside you will see a size, e.g. 58mm.
This tells you the size of screw-in filter to buy if you wish to fit one. Personally I always fit a good quality UV filter purely to protect the lens front element from damage. Brands like Hoya or B+W use good quality optical glass. Do not buy cheap filters as they will reduce image quality.
I hope this helps.