A claim, according to Law 68, is "any statement... that a contestant will win a specific number of tricks. A contestant also claims when he suggests that play be curtailed, or when he shows his cards." It may be a claim of all the remaining tricks, or it may be a claim of some and a concession of the remainder.
The same rules apply whether declarer or either defender claims. Note that it is the statement that constitutes a claim under the laws. Normally in online bridge a claim is made by pressing a button that stops play and faces the hands for the opponents to inspect; but technically, the same rules apply once a statement is made, whether the software automatically handles the claim or not. (The Swan Games software, for instance, only automatically handles declarer's claims.)
There are two basic ingredients to making sure a claim doesn't go sour:
1. Be 100% sure you know what will happen. If you can't remember for sure if a card is a winner or not -- safer to play on than to claim. If you have all the rest if a suit breaks evenly, but might lose a trick if it breaks badly -- play a couple rounds of the suit and find out how it breaks before you claim.
2. State your line of play. The purpose of a claim is to take the place of playing out the rest of the tricks. Don't just face your cards... say how you would have played it out. It doesn't have to be anything fancy. "Ruffing a club," or "3 hearts and a diamond," or "high crossruff," or whatever it is you are going to do.
After any claim, play ceases. If the claim is accepted, of course, the hand is scored up and all is well.
If the claim is rejected, the director is called and he'll do three things:
Once he has all the facts, the director announces how many tricks each side should receive "as equitably as possible to both sides, but any doubtful points shall be resolved against the claimer."
Bad claims come in two basic types: claims where some of claimer's winners turn out not to be winners after all, and claims where the claimer might actually have gotten the number of tricks he claimed, but didn't say how he planned to win them.
In the first type, claimer is assumed to follow his line of play until something unexpected happens -- for example, continues cashing his winners in the stated order until his opponent's forgotten ace or trump appears -- and after that point, the director puzzles out what the most plausible lines of play for each side are and sees what final result that leads to. The non-claiming side is assumed to play perfectly after the claim, regardless of their actual ability; the claimer is assumed to play reasonably, but not necessarily perfectly. There are particular rules about (for instance) whether or not claimer can pull an outstanding trump that he might have forgotten.
In the second type, the director considers all the lines that the claimer might have followed had he played on. This includes lines that are inferior, but not irrational. In particular, if claimer has a choice of which opponent to play for a card, as when choosing whether or not to finesse, he will "always guess wrong" (unless, for instance, he's already seen one opponent show out of a suit.)
Example: After 9 tricks, declarer has
AKQ10 in dummy and
xxxx in hand, and is about to lead from his hand. He claims the rest of the tricks.
Jxxx, 4 tricks otherwise.
This is to protect you from a claimer who, hearing his claim has been rejected, successfully guesses why the claim was rejected and then plays on to reach a better result than he would have had he not claimed: "Hmmm... I have a fistful of aces and kings, but my opponents still rejected my claim. I better play one more trump first just in case I miscounted them" or "Hmmm... I have all the rest of the tricks easily unless I get a 5-0 break in hearts... since they didn't accept my claim I had better take a safety play against a bad break."
In some simple cases it may be obvious to everyone at the table exactly what is wrong with a claim, and no harm will be done if you make the obvious correction to the number of tricks claimed and go on. But it is always better to be safe than sorry, and call the director.
Call the director, of course.
If you have conceded a trick it is impossible to lose or claimed a trick it is impossible to win, the score must always be corrected. Similarly, if all 4 players accidentally agree to a claim of the wrong number of tricks (on Swan this commonly happens if someone claims halfway through a trick and the players, but not the software, treat the trick in progress as having already been won or lost) the correct score will always be restored.
If on the other hand you have agreed to a claim for a reasonable number of tricks, but later see a different line of play that would have let your side do a trick better, you can call the director and ask him to inspect the hand; but in this case, you won't receive an automatic adjustment. The score will only be changed if there is no normal line of play that leads to the result you already agreed to.