The best way to overcome barriers is to respect the people you are dealing with. You want to understand their culture without stereotyping. Visit the country and hang out with them, for lack of a better term. Eat the food, enjoy the entertainment, take part in religious rituals. This will give you an understanding of the cultures you work with as nothing else can.
To add to the already excellent suggestions above you need to be aware of different approaches to time. Latinos, for example, are renowned for an hasta mañana attitude that can really annoy Westerners who are very punctual and fixed on set times and calendars. Likewise, some cultures are far more relational, so being friends is vital to doing business together. Such issues greatly impact the ability to conduct meetings and communicate effectively.
You might also consider having someone you trust who is a native of that culture along with you to help with these issues as well. Having lived and taught outside of the United States, I learned the hard way about cultural differences...something as seemingly small as showing the bottom of your shoe to a member whose culture finds that an immense insult could ruin your attempts at successful negotiation.
I would emphasis the importance of education here (in addition to the very good suggestions made above).
What I mean here is that you must become familiar with the important differences between your society and that of the person you are going to be talking to. This is especially important in the case of issues like eye contact and personal space -- things that can make the other person feel very uncomfortable.
Beyond that, I would recommend avoiding slang and figures of speech as well as speaking slowly and clearly (but not too much of either and not too loud -- you don't want to make it seem like you're treating them like they're dumb...).
Depending on how well you are acquainted with the culture of your client, keep in mind that verbal and non verbal communication are just as important as it is our vocabulary choice and the inflection and intonation that we give our words.
One suggestion that works for both businessmen as well as educators of students of different cultures is to share a common vocabulary. Always maintain the key words of your conversation coming up and ensure to provide written communication with every plan that is being put together.
Another great suggestion is to maintain a leveled voice, and do not over-complicate words that can easily be switched for simpler ones. This is not only for the sake of the person listening, but to avoid making you look like a "know it all."
Most importantly, do not think about the person as being any different. When it comes to business you share a common goal and understand what processes need to be followed. Two professionals speaking always speak the same language when the goal in mind is clear. Therefore, keep the goal and process simple, and enjoy the productivity that your negotiation will potentially offer.