In face-to-face bridge, a contested claim can become a rather messy affair. Unless all players agree to play the hand out, the Director may need to be summoned, and it will likely take longer than if there had been no claim.
But in online bridge, either opponent may reject a claim by simply clicking the "No" button on the popup. Play resumes from that point: no muss, no fuss, no Director calls.
When is it time to claim? When there is no doubt about the outcome of the hand. If your hand is all good, or all worthless, or all good except for one or two obvious losers: it's time to claim.
How To Claim: Click the blue Claim button at the lower left corner of the table.
A popup window will appear, asking how many more tricks you are claiming, and with space to enter any explanation. [Pro Tip: Type your explanation into the Table Chat instead; it is easier for the opponents to read there.] Your explanation might include "draw trumps" or "you get a spade" or "crossruff", just as in face-to-face bridge.
Each opponent will see a yellow popup dialog stating your claim and any explanation. If both opponents click Yes, the claim is accepted. If either opponent clicks No, the claim is rejected and play continues.
When Your Opponent Claims: A yellow popup dialog will appear, with the claim statement and any explanation. If you accept the claim, click Yes. You and your partner must both click Yes (no conferring!) for the claim to be accepted. Click No if you reject the claim, or if you don't understand it within 15 seconds or so. Your opponent will not be able to see who rejected the claim.
Defenders Can Claim Too: Either defender may Claim, or Concede (claim no more tricks), as appropriate. Declarer and defender's partner must both accept the claim; either may reject the claim.
Finally, a reminder from the Laws of Duplicate Bridge
LAW 74. CONDUCT AND ETIQUETTE. ... B. Etiquette. As a matter of courtesy a player should refrain from: ... 4. prolonging play unnecessarily (as in playing on although he knows that all the tricks are surely his) for the purpose of disconcerting an opponent.
-- Ray
Better Bridge in 5 Minutes. Guaranteed! (or the next one is free)