Respect
The simplest place to start is by treating others with the respect that you wish to receive from them. If you are either confident in your ideas or unafraid of genuinely seeking truth, then you should have nothing to fear from having your beliefs challenged and listening to others. If you are fearful, part of your subconscious already understands that your belief system is highly flawed.
Emotionally Charged Language
When a person enters a charged emotional state, such as through fear or anger, their capacity to think clearly and rationally or understand more complex concepts is reduced. If you find yourself in that state, I would suggest conquering your emotions before you continue.
Emotionally charged and aggressive language polarizes the other person, they are forced quickly into a yes/no position, whereby the only safe response is a "no." Instead if is far more effective, and respectful, to allow the other person to explore your ideas in an entirely non-committal way, and based on the logic, ethics, evidence, or substance make a far more rational decision.
Avoid Debates, Focus on Knowledge
The debate dynamic generally has very little to do withe the pursuit of knowledge or truth, and far more to do with defeating your opponent. Defeating your opponent may impress onlookers and hurt his ego, often motivating him to further strengthen his position, but rarely results in any forward progress.
Instead, I highly recommend focusing on an education and knowledge dynamic. If the purpose is to pursue knowledge and truth, then that is what the dynamic should be.
This dynamic is also useful when faced with misrepresentations or false assertions about yourself or your proposals. Often, I will take this as an opportunity to halt the discussion, and educate the other person. If the other person resists and acts uninterested in learning, there is a good chance they you are wasting your time.
Ask Questions!
When confronted with unusual or illogical belief systems and assertions, ASK QUESTIONS. Keep asking questions until either you understand their perspective, the flaw in their assertion is glaringly obvious, or they discover the holes for themselves. Better yet, it saves time!
It is also significantly more respectful to ask questions, compared to many other alternatives. Asking questions will also grant you insight into their point of view and values, and allow you to communicate more clearly and effectively with them.