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I too would like to know. However, I think it just depends on how many votes you receive on your article, because each of the editors picks have quite a bit of votes. So it might just be popularity based, but I am not certain.
I found to become "Editor's Picks of The Day" from bloggers faq.
Steps:
a. Complete your user profile. We encourage well written text that describe your interest. Too short profiles means lack of seriousness. User profile must not contain any URL or Email. Go to User Dashboard > Edit Profile for updating your profile.
b. User must change default Avatar and complete other fields in Account. Avatar with real pictures will get better chance.
c. Blog information should be correct and Submitter must Own the Blog. In case we find it suspicious we may ask to show proof of ownership.
d. Any profile or site solely for internet marketing or affiliated marketing will get less chance to be the featured Blogger.