NEWBIE QUESTION: Key space exhaustion - How do I know when I'm there?

Suppose I'm trying to crack a cipher system by exhausting the key
space. How do I know when I've got the correct key value? The
obvious answer is look at the plaintext generated, and if it makes
sense, you've cracked it, if not try the next possible key value. How
exactly do you check that the resulting plaintext "makes sense"? I
guess if you expect the message to be in English, statistical analysis
on the plaintext is the way to go. I don't know how time consuming
this step is.

I think I read somewhere that key exhaustion is done
probabilistically: Possible candidates for the correct key are
eliminated from improbable ones statistically (??) Is this true? If
so how exactly? Partial statistical analysis of plain text?? I
thought one of the properties of a good cryptosystem is you can't find
out how close the proposed key is to the actual one, i.e. you have to
guess all the way, guessing part of the way won't help.