It's important to note that all of the 'images' of the stars that are not the Sun in that slide show are not actual telescope images (apart from the Eta Carina nebula that is actually much bigger than that slide show suggests?). They look like either drawings or re-coloured images of the Sun to give an idea of what that star might look like. We cannot resolve any star other than the Sun with a single telescope (even the biggest and best we have) although we can get some information about sizes using interferometry with multiple optical telescopes. These techniques still don't give you the kind of detail implied in that slide show. Not being critical of it, it's quite cool, but just bear that in mind since it isn't clear from the images alone.
What is normally done to estimate the size of a star is to measure its temperature by measuring its colour (blue is hotter than yellow which is hotter than red). We then have theories that tell us based on the colour and type of star (which we can determine by other aspects of the spectrum) how big the Star must be. These theories have been checked and calibrated on stars where we can measure the size directly, either through eclipsing binaries or optical interferometry (google or ask for more info on any confusing or new terms!) so we have some confidence that they work for stars were we can't get such direct information.