Bear in mind, it must be dark in order for Speedy Spirits to spawn, and some can only be captured during the blackout.
Spirit #1
Wardrobe Room
To find the first Speedy Spirit, simply tap on the wardrobe on the far-right of the room.
Spirit #2
Study
To find the second Speedy Spirit, tap on Neville's chair behind his desk. Before attempting to get this spirit, make sure to vacuum up the flying books.
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Breaker Room
To find the third Speedy Spirit, tap on the table on the far-left of the room.
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Storage Room
To find the fourth Speedy Spirit, tap on the chair closest to the door.
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Dining Room
To find the fifth Speedy Spirit, tap on the cabinet on the left side of the room.
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Kitchen
To find the sixth Speedy Spirit, tap on the dishwasher on the left side of the room.
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Gym
To find the seveneth Speedy Spirit, tap on the exercise bike closest to the front wall.
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Nana's Room
To find the eighth Speedy Spirit, tap on the armchair on the right side of the room.
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Billiards Room
To find the ninth Speedy Spirit, tap on the chair in the corner of the room. This must be done while Slim Bankshot is there.
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Twins' Room
To find the tenth Speedy Spirit, suck the top bunk with your vacuum.
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Music Room (During Blackout)
To find the eleventh Speedy Spirit, tap the pianist's chair.
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Hidden Room (During Blackout)
To find the twelfth Speedy Spirit, tap the chest on the far right.
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Nursery (During Blackout)
To find the thirteenth Speedy Spirit, tap on the crib.
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Cellar
To find the fourteenth Speedy Spirit, tap on the crate beside the door.
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Sealed Room
To find the fifteenth Speedy Spirit, tap the chest closest to the banister.