Consider the Source
The other person might be speaking from some authority. They may actually know what they're talking about. In that case, they're worth a listen to. Even if they're not experts, they might be worth a listen to anyway. It's important first to understand what it is they're actually trying to say, before we counter offer our own opinions.

Consider your source
Are you more knowledgeable than they are? Do you have facts to support your point of view? If you have good backing, then feel free to speak from authority. Be careful though; our perspective only seems right because we're closest to it. Make sure you let it be known where you're coming from. Even if they disagree with your source, they can't really argue if you say "the way I see it is…"

Approach the disagreement appropriately
Some people become defensive when confronted with disagreement. They won't listen to you, no matter what you say. Others like the dialogue. Again, it's about considering the source and deciding if "winning" is important.

Value the relationship more
Remember that there is a person behind that opinion. If they mean something to you, value it more than being "right." Many times you don't have to be "right" to win. Conversely, if they really are "wrong" and you value the relationship more, helping them to find a better "right" answer is appropriate.

Make sure you both get something out of the disagreement
Disagreements can rip people apart. Don't let that happen. It's really okay for two people to see things differently. Take away some lesson from all this. Ask yourself if you learned something by seeing someone else's point of view. Sometimes disagreements can actually help you strengthen your resolve. Agree or not, but grow either way.