Realize that there is nothing wrong with being wrong. As we all know, no one is perfect so at some point or another we will all be mistaken. Since this is the case it only makes sense that admitting you're wrong is not a big deal; after all, it happens to everyone. There is only a problem when you don't acknowledge it and try to improve.
Thank the other person for being understanding in advance. Really, he should be glad that you've admitted your mistake but if you thank him in advance he really has no choice but to be understanding.
Alexander Pope, the poet, once said "No one should be ashamed to admit they are wrong, which is but saying, in other words, they are wiser today than they were yesterday." This is really the essence of this post; being wrong is nothing to be ashamed of, but not admitting it is.
When is a time that you have been wrong and had to admit it? How did you handle it? What tips do you have?