Resolution is a very important consideration for a modern telescope, but actually not a particularly difficult one to understand. There are two factors that determine the resolution of a telescope:

1) The so-called "diffraction limit" of the telescope which depends upon the size of the main mirror or lens, with bigger being better.

2) The "blurring" effect of the atmosphere - usually called "seeing".

In general, for smaller telescopes, the first is the most important effect, whereas for large, professional telescopes the "diffraction limited" resolution is so good that the "seeing" effects of the atmosphere tend to dominate.

Let's look at the simplest observing instrument - the eye. The pupil of the eye has a diameter (at night) of about 5mm. This gives a resolution of about 30 arcseconds (a degree is divided into 60 arcminutes which are then divided into 60 arcseconds, giving 3600 arcseconds in a degree).

The lines of the letters in a newspaper are typically about 1/4 mm wide, so someone with excellent vision could just read a paper if it was about 2m away.

For a small telescope, the diameter of the main mirror might be, say, 10cm. This gives a much better resolution of just 1.5 arcseconds, so using the telescope you could read the paper even if it was over 40m away (from near the centre of a football pitch to the goal).

However, even on the very best observing sites, the atmospheric "blur" (seeing) is rarely gives resolutions better than about 0.6 arcseconds. So, even with a very large mirror, you would still only be able to read a newspaper about 100m away.

Of course, if you put your telescope in space, like the Hubble Space Telescope, you do not have to worry about the atmospheric effects and you get back to "diffraction limited" images. For the HST, which has a mirror 2.4m across, the resolution is an amazing 0.06 arcseconds - so you could read your newspaper about 1km away!

Given the problem of atmospheric "blurring", you may ask why we build such big telescopes on the ground, and the answer comes not in resolution but *faintness*. The bigger your telescope, the more light it can "collect", so the fainter the objects is can see. For example, the Liverpool Telescope that you can use as part of the Sky Watch project, has a 2m diameter mirror. Than means it collects 160,000 times as much light per second as your eye. When you put a really good electronic CCD camera on the back and take long exposures, that means it can detect stars many millions of times fainter than anything you could possibly see for yourself unaided!

Finally, you ask about the resolution of radio telescopes. So far I have only talked about optical telescopes. The diffraction limit of a telescope does not depend only on the size of the mirror or lens (or dish for radio telescopes) but also the wavelength of the electromagnetic radiation. For long wavelengths like radio waves, the resolution is much worse for the same size of telescope. Even for very big telescopes like the Lovell Dish at Jodrell Bank in the UK or the giant Arecibo Telescope (star of many films!) the resolution is very poor compared to optical telescopes - Arecibo is usually working at a resolution of nearly an arcminute (60 arcseconds).

One way around this problem for radio telescopes is to cleverly combine the signals from several telescopes using a technique called "interferometry". Here the resolution depends on the distance between the telescopes, not their size, so you can get very high resolution observations - for example by using telescopes on opposite side of the world. There is not a lot of work going into developing similar systems for "normal" optical telescopes, although it is much harder at the short wavelengths of "visible" light.