How is the observable universe mapped? As I was looking at how big earth was relative to everything else in the universe, this picture boggles my mind.
http://en.wikipedia.org/wiki/Observable_Universe#Horizons
We're like the size of an atom relative to earth in relation to the universe.  Is this picture just an interpretation or is it how things really are?
How is it possible to map things like this? Up to the Solar Interstellar Neighborhood seems understandable to me.  Then it shows that this neighborhood is only a tiny tiny little dot in the Milk Way in this specific location relative to the other little dots.  Then it shows our galactic group part of the local galactic group, to the Virgo Supercluster, to the Local Superclusters, etc.
 A: To build up a plot like you see in your link, one simply finds the celestial co-ordinates for all objects discovered. Once you have these, you simply plot them!
The azimuth and altitude of an object $\theta$ and $\phi$ are found either by correcting observed azimuth and elevation for Earth's know orientation or, more reliably, by calibrating the azimuth and elevation measurement with known objects, then inferring those of the hitherto unknown object. 
Then a range of techniques are used to find $r$: parallax out to a few hundred light years, then use of standard candles such as Cepheid variables for further away things and lastly measuring redshift and "calculation" from Hubble equation. See the Wikipedia article on the Cosmic Distance Ladder.
A: Honestly, the universe really is that big! Well, we assume/model that it's actually bigger (the un-observable universe). Some diagrams and such may not be to scale, but I imagine that one and similar ones are - and the sizes and scales are just mind-blowingly large, and that really humans aren't made to be able to conceptualise that size.
In terms of actually detecting the stars, black holes, planets and other cosmic objects - it's essentially pointing a telescope in the sky and seeing what there is. Space telescopes like the Hubble are good for this, as are many earth based one. By looking at the whole electromagnetic spectrum (from gamma to radio waves) we build up the picture. The reason we can't see beyond the observable universe is that the universe hasn't existed for long enough for the light any further out to reach us.
