Rebuke the Talkers
Question: In the synagogue where I pray there are a couple of individuals who cannot refrain from carrying on a conversation during the Repetition of the Service and the Reading of the Torah. I am aware that this is wrong and that it should be stopped. What is the right way for me to achieve this?
Answer: When people do what you describe they are not only violating the halacha by showing such vulgar disrespect for the sacred activities taking place in such holy surroundings, but are also guilty of denying those around them the ability to properly concentrate on what they are hearing. It is for this reason that the Shulchan Aruch (Orach Chaim 124:6) rules that such people should be rebuked. Your question, however, is what is the most effective way of achieving results.
The first step, of course, is to try talking to them, one at a time, and pointing out the gravity of their irreverence, stressing its damage to you. This is important because the same person who will respond negatively to reproof about his religious behavior will usually be prepared to accommodate the needs of a fellow worshipper.
But even if you succeed in gaining a begrudging commitment to stop the gabbing, the battle isnt over. The temptation to swap the latest news may easily cause the gabbers to forget their promise. Your reminder to them can come in the form of a "Shah!" or a frown in their direction, or by pointing to one of those signs prominently displayed in many synagogues which warn against such behavior.
The main thing is dont give up! People who come to pray in the synagogue have a basic appreciation of their responsibilities to G-d and to their fellow worshippers. If they occasionally succumb to the temptation to talk when they should not, it does not mean that they are incapable of improving their behavior if you continue to monitor them gently but firmly.