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.
Breaker Room
To find the third Speedy Spirit, tap on the table on the far-left of the room.
Storage Room
To find the fourth Speedy Spirit, tap on the chair closest to the door.
Dining Room
To find the fifth Speedy Spirit, tap on the cabinet on the left side of the room.
Kitchen
To find the sixth Speedy Spirit, tap on the dishwasher on the left side of the room.
Gym
To find the seveneth Speedy Spirit, tap on the exercise bike closest to the front wall.
Nana's Room
To find the eighth Speedy Spirit, tap on the armchair on the right side of the room.
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.
Twins' Room
To find the tenth Speedy Spirit, suck the top bunk with your vacuum.
Music Room (During Blackout)
To find the eleventh Speedy Spirit, tap the pianist's chair.
Hidden Room (During Blackout)
To find the twelfth Speedy Spirit, tap the chest on the far right.
Nursery (During Blackout)
To find the thirteenth Speedy Spirit, tap on the crib.
Cellar
To find the fourteenth Speedy Spirit, tap on the crate beside the door.
Sealed Room
To find the fifteenth Speedy Spirit, tap the chest closest to the banister.