At duplicate bridge, it is polite to greet each pair of opponents you face. You are not expected to exchange handshakes and huge grins, but bridge after all is a game and salutations are appropriate. At the end of a round, it is also common for either pair to say "thanks" or "good luck." Only at extremely high-level competitions would you not expect many pleasantries.
During the play of the hand, whether it is regular or tournament bridge, talk is usually kept to a minimum. Declarer can call for cards from dummy, and she, along with the defenders, may claim (to win a surefire, specific number of tricks) at any time. Aside from that, players normally do not chat until the hand is finished. Dummy especially should never say anything to assist declarer. The only thing dummy is allowed to do in tournament bridge is to ask partner if she is void when she fails to follow suit. Dummy is NOT allowed to make or suggest a claim.
When a hand is over, you can compliment any player who did something particularly well, either in the bidding or the play. If you are praising partner, be sure not to overdo it because this may be perceived as gloating (particularly if the opposition made a mistake). It is also considered proper manners to refrain from criticizing partner for some wrong action he took. Squabbling after a hand makes the game less fun for everyone at the table. It also delays the play of the next deal.