The term "sly man" refers to G.I. Gurdjieff's Fourth Way system, a method of spiritual development that combines the physical (fakir), emotional (monk), and mental (yogi) paths simultaneously and within ordinary life, rather than separately. The "slyness" comes from this integrated approach, which allows a practitioner to work on all aspects of their being at once to achieve accelerated spiritual growth, hence outstripping the partial development of the separate ways.

DO THIS, NONSTOP:
self-remembering
be conscious of how the body moves, what it does, what it feels
observe the body, nonstop
it counteracts sleepiness, daydreaming
AUTOMATON
brings the mind and body closer
(early stages, then move on to the next stages, look it up)

central:
you do not remember yourself
you do not feel yourself
you are not conscious of yourself
with you
it observes, just as it speaks, as it thinks, it laughs
you do not feel: I observe. I notice. I see.

The Fourth Way as the "Way of the Sly Man" 
Integration: Unlike the other ways that require withdrawing from the world, the Fourth Way is designed to be practiced while living a normal life. It integrates the development of the body, emotions, and mind instead of focusing on one at a time. 
Simultaneous work: The "sly man" knows a secret: to work on the physical, emotional, and mental aspects of the self in parallel. This saves time compared to the other three paths, which require years of dedicated work on one aspect alone. 
Balanced development: By harmoniously developing all three sides of his being, the practitioner can achieve a more complete and balanced state of self-awareness and will, which is the ultimate goal of Gurdjieff's teachings.

Key concepts
Self-awareness: The core of the practice is to develop conscious awareness of one's mechanical actions and thoughts through "self-remembering". 
Ordinary life: The Fourth Way uses the challenges and demands of daily life as the very material for inner work and transformation. 
"Born asleep": Gurdjieff taught that most people live their entire lives in a state of "waking sleep," unaware of their true potential. The Fourth Way is a method to awaken from this state.