Magnification, resolution, numerical aperture - to be perfectly honest, we're a little confused too. But we think we can get you on the right track to figuring out what kind of microscope you have your hands on or are thinking about buying.
Finding the actual magnification of your microscope is easy. If you have a compound microscope with a rotating nosepiece, the magnification will be engraved on the barrel of each objective. For the eyepiece, check for the magnification at the top. Simply multiply both numbers to get the total magnification for each eyepiece and objective combination.
The resolution, on the other hand, is a bit harder to get your head around. It is reflected in the lens' ability to form separate images of lines or dots. It is dependent on the objective lens alone, since the eyepiece does nothing more than magnify the image it is given.
You can magnify something all you want, but going higher than 1000x is pretty useless. Past this point, the wave nature of light puts a theoretical limit on resolution for microscopes. This is somewhere in the neighborhood of 250 nanometers, plenty small for anything you're doing. An electron microscope will get you magnifications of up to 1,000,000x, but it'll also get you a hefty mortgage.
The numerical aperture is closely related to resolution and magnification. It is directly proportional to both, meaning the higher the magnification, the higher the numerical aperture. The figure refers to the lens' ability to increase the resolution by collecting a wider cone of light from the specimen. As high-powered objectives approach a specimen, they must collect more light, meaning the numerical aperture (essentially the hole through which light passes) must by higher. For very high powered microscopes, this number is around 1.4. Lower powered microscopes have a numerical aperture around 0.04. The number is usually engraved on the barrel of the objective, by the magnification. You'll recognize it because it won't be followed by the "x."
Finally, a condenser also has a numerical aperture, and it must meet or exceed the aperture of the objective lens to properly light the specimen. Higher powers of microscopes will therefore need condensers which also have higher numerical apertures.