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Note: This is just a general explanation for Reasoning because I don't remember Gilford's exact text. And if someone explained this already, my apologies. I'm typing this up on my DS, which takes quite a while.
It depends on how the monster can be summoned. If it can be normal summoned, stop picking up cards and follow the rest of the instructions; otherwise, keep picking up cards until you reach another monster and recheck the summoning conditions.
If the monster doesn't have a restriction on Special Summoning ("This card cannot be Special Summoned" or "This card can only be Special Summoned by"), summon the monster if the number doesn't match, and dump the other cards. If the number matches or the monster has one of the restrictions (like Ancient Gear Golem or Sky Scourge Invicil), dump everything.