1. Listen & be understanding
Don't just say "I disagree", show them that you understand them before you explain your opinion.
I see what you mean, but...
I agree up to a point, but
2. Avoid negative words - instead use positive words in a negative form
Don't say: I think that's a bad idea.
Say: I don't think that's such a good idea.
3. Say the magic word: Sorry
This word can be used in many ways: to interrupt, to apologise, to show you don't understand, to disagree. It diffuses tension and it allows you to start a statement more comfortably.
Sorry, but I don't really agree
4. Use little words to soften your statements
Break down negative sentences with some softeners.
Don't say: I didn't catch that
Say: Sorry, I didn't quite catch that
5. Avoid statements with the word 'you'
This is aggressive and too direct. But put the focus on 'I' or 'we'.
Don't say: You don't understand me.
Say: Perhaps I'm not making myself clear.