702.91a Miracle is a static ability linked to a triggered ability (see rule 603.10). "Miracle [cost]" means "You may reveal this card from your hand as you draw it if it's the first card you've drawn this turn. When you reveal this card this way, you may cast it by paying [cost] rather than its mana cost."
The window of opportunity is very small, you must cast the card before it reaches your hand. As soon as it touches the other cards in your hand it is too late. This is perhaps a little less clear if it's the only card you have at that point, but you still need to cast it as you are drawing it.
Some players may Sylvan Library, which also affects draws in a very strange way. Miracles do not fall in to any of the traps that Sylvan Library presents. I think a lot of people will misunderstand Miracles, but the mechanic has actually been very well designed and I don't think it should cause any problems.