Everyone's different. We all have different parents, different upbringings and different values. However, we also need to be around and work with other people to function in society. The key to bridging this gap is effective communication.
Although speaking is the first action that comes to mind when one hears the word "communication," it's actually just half of the equation. Equally--if not more--important is listening. Rather than passively listening and just letting information flow at you, listen actively. Relax your body, maintain eye contact and keep interruptions to a minimum. When you do interrupt, do so at a pause and only to paraphrase to clarify what the person is saying. The speaker will feel that his message is being better received by an attentive listener--because it is.
Keep your body open. Don't cross your arms or legs, but keep both outstretched, indicating receptiveness.
Empathy and Personal Responsibility
Show empathy and take responsibility. The person you're speaking to needs to feel that you understand what he means and not feel threatened. One of the best ways to do the former is to use the paraphrasing strategy mentioned above. Taking responsibility relies on one word: "I." Never use "you" when discussing something negative--for example, "you made a mistake" sounds more confrontational than "I'm having a hard time understanding," although the message is ultimately the same.
Clarity is so important in effectively communicating that it deserves its own section. It's a tricky thing to do, too; you need to use enough words to get your point across without assuming that the other person has information he doesn't, but you also need to economize so that your point isn't lost or muddled in a sea of unnecessary words.
If someone is angry, don't try to deduce the cause of or a solution to the anger until he has calmed down. People usually just need to be heard out when they're angry, so let them talk, only speaking to give compliments. A resolution can be pursued later.