How big is the observable universe, and why can't we see any further?
45 billion light years
The universe is 45 billion light years in all directions. The word "see" is a bit of a misnomer. What we are doing in fact is "detecting." For example, you cannot see the radio waves (which are a part of the light spectrum) but you can detect them with your television. The same is true of the most distant parts of our universe.
We cannot see any further right now because our technology is not sensitive enough to do so. That assumes there is a "further" which I happen to believer there is.