Make your case simple and clear. If you write down the main points first, you are less likely to jumble them up.
Ensure that your facts are correct. If one element of your case is shown to be false, it will reduce the credibility of everything else you say.
Listen to the other person. Let them share their views in full before you make your case. They will be more likely to listen to you, and you can alter what you say to address their concerns.
Dig deeper. Find out why they hold a different view. You may be able to meet their real needs (eg, wanting you to consider them an equal) in another way, allowing them to be convinced by your argument more easily.
Ask questions. People are much more likely to change their mind if they have talked through your argument themselves rather than just listened to you presenting it.
Appreciate the other person's aspirations. Link your position with their values - emotional reasons can be just as powerful as rational ones.
Give compliments. Make the other person feel good about themselves without being obvious or obsequious.
Show that others agree with you - it can help support your case but is rarely sufficient to win the argument. When was the last time you chose a supplier entirely because of their client list?
Separate the argument from the person. Differentiate between the substance of the disagreement and the two of you as people. Focus on what they are saying (they believe advertising has no effect), rather than what you think about them as a result of their position (they are stupid).
People make decisions for their reasons - not yours. Adapt your argument to the person you wish to convince.