Why are they praying to a deceased human being instead of to God? Why not ask God for His help?
Catholics and some other Christians believe that the ability to make intercession on others' behalf, before the throne of God's Mercy, does not end with death. In fact, one's ability to make intercession is increased. If David, while alive, was a man after God's own Heart, how much more he is while beholding the face of God!
If you read the Franciscans' prayer (above) carefully, it is addressed to God the Father, and it incorporates His Son, Jesus Christ, and also the Holy Spirit. It asks that if it is God's will that He should glorify his servant, Archbishop Sheen, then, please hear and answer the intercession that he is making for this cause.
It is important to see that this prayer acknowleges God as being the Source, and the Almighty, to whom we owe all love, worship, praise, loyalty, obedience, and thanksgiving. For God to "glorify his servant," means that through the answer that God gives to us as a result of Archbishop Sheen's intercession - through the granting of this miracle - God is testifying as to the holiness of his servant, and the esteem in which He holds him.
In turn, this takes NOTHING away from God - it is a glory to Him. It glorifies God when He can say, "This is my good and faithful servant, in whom I am well pleased." By asking Archbishop Sheen for his intercession, we are actually glorifying God by acknowleging His accomplishment of grace in Archbishop Sheen's life for his salvation - we are giving Jesus' Passion and Death the glory, and also the lifelong working of the Holy Spirit in this man's soul, and in ours, too.
"Why are they praying to a deceased human being instead of to God? Why not ask God for His help?"
Very good question.
He did win a popularity contest but only God knows what is in a person's heart and mind.