I've refereed at least a dozen papers in my (short) career so far and I still find the process completely baffling.  I'm wondering what is actually expected and what people tend to do...

Some things I've wondered about:

1) Should you summarize the main results and or the argument?  If so, how much is a good amount. What purpose does this serve?

2) What do you do when the journal requests you to evaluate the quality of the result (or its appropriateness for the journal)?  Should one always make a recommendation regarding publication? 

3) What to do about papers with major grammatical or syntactical errors, but that are otherwise correct?  Does it matter if the author is clearly not a native English speaker?

4) On this note, at point does one correct such mistakes?  Ever?  If there are fewer than a dozen? Should one be proof-reading the paper?

5) What do you do when you do not understand an argument?  Does it matter if it "feels" correct.  How long should one spend trying to understand an argument?

6) What to do about papers that have no errors but whose exposition is hard to follow?

I've been spending a fair amount of time editing a journal this year, and it's pretty
amazing what different people think of as a "referee report".  The first thing you should 
keep in mind is that the editors will be incredibly appreciative if you 
look at the paper in detail and send in comments in a timely manner, whatever
the comments are.    In my mind a good referee report begins with a very short (a few sentences) summary of the result and the argument.  It includes an opinion on whether 
the result and proof are (i) correct (ii) readable (iii) 
interesting to lots or only a few people; also (iv) a recommendation on whether
it is good enough to appear in the given journal, or alternatively/also
comparisons to the quality of one or two other recent papers in the field, 
or just a statement that the referee isn't sure if it is good enough or not, and 
(v) a non-empty list of specific corrections/suggestions.
Re (3-4) it's perfectly fine to send in a one-line request that the paper be revised
so that it is written in correct English.  It's not your job to correct
grammatical mistakes if there are more than a few.   Re 
(5-6) if an argument is hard to follow, you can just ask for a revision in which the authors explain more.    As an editor, it's quite easy (with computers and e-mail being what they are) to request a revision, even after the referee has only read 
part of the paper. 