How do I referee a paper?
To the best of your knowledge, does the paper make a significant, well-presented, and correct contribution to the state of the art?  If the paper fails any of the three criteria, it's fair to reject it for that reason alone, regardless of the other two.
Here's what I think a report should contain.  Everything should be visible to the author, except possibly for serious accusations of misconduct.

a. A quick summary of the paper, to help the editor judge the quality of the results, and to help convince both the author and the editor that you actually read and understood the paper.  Place the result in its larger context.  Include a history of prior versions, even if the authors include it in the submission.  Be respectful, but brutally honest.

b. A discussion of the strengths and weaknesses of the paper, in terms of correctness, novelty, clarity, importance, generality, potential impact, elegance, technical depth, robustness, etc.  If you suspect unethical behavior (plagiarism, parallel submission, cooked data), describe your suspicions.  Be respectful, but brutally honest.

c. A recommendation to the editor for further action — accept, accept with minor revision, ask for a second round of reviewing, or reject outright.  Keep in mind that you are making a recommendation, not a decision; if you can't make up your mind, just say so.  Be respectful, but brutally honest.

d. More detailed feedback to the author — more detailed justification for your recommendation, requests for clarification in the final version, missing references, bugs in the proofs, simplifications, generalizations, typos, etc.  Be respectful, but brutally honest.
Conference reports should be shorter; program committees have hundreds of papers to consider at once.  Whether there should be a difference between conference and journal papers is up to the journal (and indirectly, up to the community).  Most theoretical computer science journals do not insist on a significant difference; it is quite common for the conference and journal versions of a theory paper to be essentially identical.  When in doubt, ask the editor!
If you still don't understand the paper after making a good-faith effort, it's the author's fault, or possibly the editor's, but certainly not yours.  The author's primary responsibility is to effectively communicate their result to their audience, and a good editor will send you a paper to referee only if they think you're a good representative of the paper's intended audience.  But you do have to make a good-faith effort; do not expect to immediately understand everything (anything?) immediately on your first reading.
If there are a lot of errors, don't even read the paper; just recommend rejection on the grounds that the paper is not professionally written.  Otherwise, if you really want to be thorough, include a representative list of grammar, spelling, and punctuation mistakes, but don't knock yourself out finding every last bug.  Be respectful, but brutally honest.
Expect to spend about an hour per page, mostly on internalizing the paper's results and techniques.  Be pleasantly surprised when it doesn't actually take that long.  (If it takes significantly less time than that, either the paper is either exceedingly elegant and well-written, you know the area extremely well, or the paper is technically shallow.  Don't confuse these three possibilities.) 
You should write at least as many referee reports as other people write for you.  If this takes more time than writing your own papers, you're not spending enough time on your own papers.