We had a 4-board match this week where eight Division One chessplayers weren't clear enough about the rules to give much confidence in the knowledge of the rest of you... 

Stewart Reuben says in the latest Organiser's Handbook that this rule "...continues to give arbiters problems. ... When I was in South Africa and held a seminar, the local arbiters wanted to spend the whole time discussing nothing else."

So, Article 10 of FIDE Laws of Chess covering most forms of chess (including rapidplay but not blitz) says:

Article 10: Quickplay Finish

• 10.1 A 'quickplay finish' is the phase of a game, when all the (remaining) moves must be made in a limited time.
• 10.2 If the player, having the move, has less than two minutes left on his clock, he may claim a draw before his flag falls. He shall stop the clocks and summon the arbiter.
• a. If the arbiter agrees the opponent is making no effort to win the game by normal means, or that it is not possible to win by normal means, then he shall declare the game drawn. Otherwise he shall postpone his decision or reject the claim.
• b. If the arbiter postpones his decision, the opponent may be awarded two extra minutes and the game shall continue in the presence of an arbiter, if possible. The arbiter shall declare the final result later in the game or after a flag has fallen. He shall declare the game drawn if he agrees that the final position cannot be won by normal means, or that the opponent was not making sufficient attempts to win by normal means.
• c. If the arbiter has rejected the claim, the opponent shall be awarded two extra minutes time.
• d. The decision of the arbiter shall be final relating to 10.2 a, b, c.

You will not have overlooked that a range of positions where it is not possible to win by normal means is not given and a definition of 'normal means' is also not to be found.  That's law-making for you, and it is never beyond the ingenuity of chessplayers to come up with borderline and contentious cases no matter how much clarity you try to give.  The Preface to the Laws of Chess appeals to us all:

The Laws of Chess cannot cover all possible situations that may arise during a game, nor can they regulate all administrative questions. Where cases are not precisely regulated by an Article of the Laws, it should be possible to reach a correct decision by studying analogous situations which are discussed in the Laws. The Laws assume that arbiters have the necessary competence, sound judgement and absolute objectivity. Too detailed a rule might deprive the arbiter of his freedom of judgement and thus prevent him from finding the solution to a problem dictated by fairness, logic and special factors.

Moreover, while in a weekend Swiss you will have someone in the role of arbiter, at a club match, you will not.  But we have guidelines in Appendix D:

D. Quickplay finishes where no arbiter is present in the venue.

Where games are played as in Article 10, a player may claim a draw when he has less than two minutes left on his clock and before his flag falls. This concludes the game.
He may claim on the basis:

1. that his opponent cannot win by normal means, and/or
2. that his opponent has been making no effort to win by normal means.

In a) the player must write down the final position and his opponent verify it.
In b) the player must write down the final position and submit an up to date scoresheet. The opponent shall verify both the scoresheet and the final position.
The claim shall be referred to an arbiter whose decision shall be final.

I've heard reference to "WECU guidelines for events at which no arbiter is present" but I don't think I've ever clapped eyes on it.  I'll update this page if I can find it. 

There's a chap from West London Chess Club, Edward Tandi, who had a little go at fleshing this out in recent years, which I found helpful and included examples: http://www.westlondonchess.com/FIDE_10_2

And the Arbiters have has some discussion about it: http://chessarbiters.co.uk/QP.aspx
Including the guidance: "In a match between two teams the respective captains should attempt to reach a decision; otherwise the evidence should be submitted to the person designated in the tournament rules."

Stewart's Handbook apparently gave some example positions but I haven't laid my hands on that version, just the text-only out-of-date version from ChessIQ.com.

White played Be4-g2 and his flag fell; Black sportingly agreed a draw.