According to the NASA astrophyicist Paul Butterworth the observable Universe is about 10 billion light years in radius.
He says that “This number is obtained by multiplying how old scientists think the Universe is by the speed of light. The reasoning there is quite straightforward: we can only see out to that distance from which light can have reached us since the Universe began.”
However he does also say that “The observable Universe may be only a small part of the physical Universe. In some theories, the Universe may have expanded very fast just after the ‘big bang’, and only a little bit may have remained within range of detection.” In which case, as Drew says, you can’t really measure it with any certainty because you don’t know if you are missing something just a little bit further out!! 🙂
But it basically involves calculations of the age of stars and their current distance from us! 🙂