I'm one of those that hold the universe is finite but undefined. The edge of the universe in that model is constantly changing, so its hard to put your finger on it. Sort of like the old example of a fractal... trying to measure the shoreline of an island as wave action constantly rearranges the sand on the beach, only the universe appears to be expanding at this time based upon the Doppler shifts of distant objects, so its rearranging itself outward.
Also I think its quite possible to consider the edge of the universe from both sides, inside and out, as the same surface like that of a Kline bottle, the inside surface is twisted through a higher dimension so its actually the outside surface. So is it also fluctuating in an inward direction when looked at from the other side if its going outward from this side?
As for finding the edge, the distance there from here would be equal to the age of the universe which depending upon the model used (the arguments over the distance modulus come in here), current theories predict between 10 and 20 billion years (light years), or at least the last time I checked. 25 years ago when I was in college we used to laughingly refer to a "Sagan unit" as a billion of something.
So don't know if that means we found the side of the dish, but sure enough there is plenty for the cosmologists to argue over about when and if we can. Its remarkable that the mind can get itself wrapped around such a concept and that were it not for other things we've done with our minds to get us to the point of such luxury, we'd be occupied with important stuff such as looking for food or avoiding becoming food.
As for the alien factor in all of this, I think the last sentence in the paragraph above is where monolith appears... 
mole
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mole
Who is John Galt?
