up to 7NT; "call" is a collective term for bids, doubles, redoubles, and passes.)This depends on several things: what caused you to make the call or play, why you want to change it, and how quickly you ask for the change to be made.
The rules are somewhat different for taking back a call than for taking back a card, so we'll look at each in turn. (Why "call" and not "bid?" It's a technicality: "bid" refers only to the 35 number-and-denomination calls from 1 up to 7NT; "call" is a collective term for bids, doubles, redoubles, and passes.)
If your opponents have mis-explained their auction to you and you wish to change your call after receiving the correct information, your side's most recent call can be taken back without any penalty. If you would have bid differently earlier in the auction, the director won't let you take back your bid, but may adjust the score if you were damaged by the misinformation.
Also, if your right-hand opponent misclicks, but doesn't notice until after you call but before your left-hand opponent does, you will be able to change your call once you see what RHO intended to bid.
For further details, see Law 21.
If you intended all along to make one call, but accidentally clicked on another, and you stop the auction and notify the director before your partner has called again, you'll be allowed to change it. It doesn't matter if your left-hand opponent has called again too, as long as your partner hasn't. (If you change your call, your LHO will also be allowed to change his without penalty.)
Even if your mistake is completely innocent, if you don't notice the mistake until after your partner has bid again, it is too late to change it. In this case, you must not say a word about having misbid until after the auction is over (if your side declares) or until the end of the hand (if your side defends)!! If you remain silent, your partner will make sense of the bidding as best he can, and you can bid whatever you wish at your next turn to try to recover. If you reveal to the table that you have misbid, however, you give your partner unauthorized information about your hand -- this severely limits your partner's choice of bids and plays for the rest of the deal and can lead to an unfavourable score adjustment.
The right to correct a misclick described above applies only to a purely mechanical error. If you thought your partner's 4NT was natural, passed, and now believe it was Blackwood, or you thought you were responding to partner's opening instead of overcalling an opponent's opening, your call cannot be taken back without incurring some substantial penalties.
Let me emphasize this point once again: if you have misbid but can't change your bid, it is in your best interest to remain silent. Neither your opponents nor your partner is entitled to know what you've done wrong yet, and speaking up will only help your opponents and subject your partner to possible penalties.
The details of when calls can or can not be retracted are in Law 25.
In general, it cannot.
In face-to-face bridge, there are certain rare occasions when this is possible. Most of these are after leads out of turn, or in the process of correcting revokes, or when dummy mis-hears the card declarer called for him to play. In online bridge these situations never arise.
A card is played when it is "detached from a player's hand and faced on the table immediately before him." Once the card is out where the other players at the table can see it, you are committed to it.
If you are a defender, as with uncorrectible misbids, if you misclick, it is your responsibility to remain silent, so as to avoid conveying unauthorized information to your partner about your hand. If you are declarer, there isn't any UI penalty (dummy doesn't get to take part in the play anyway), but neither the director nor your opponents are obligated to let you take back the misplayed card.
The details of when a play can be retracted are in Law 47.
Special rules apply following a claim. In general, if you simply click on the wrong number of tricks when the claim dialog box pops up and the claim is accepted before anyone notices the problem, the error is corrected. If you change your mind about how you want to play the hand after you have claimed, on the other hand, you will usually be held to your original line of play. For details see the section on claims on this page.