But if I were to speculate, the lateral and premotor cortex is the area of conscious thought about movement. It's not separate from your consciousness since it is part of your consciousness.
Speculation aside, is there not room for error between the conscious wish and the movement (muscular contraction)? But if we don't know what is between...?
Sigh... looks like I'm pulling out my old anatomy texts haha

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So first I should mention, they aren't entirely sure how the premotor cortex starts a movement, but we do know it has connections directly with the spinal chord, and it connects with the primary motor cortex.
But if you're wanting to know what happens what you decide to start a movement, and you make that movement happen, you have to zoom in to the nerve, and then zoom in further to the individual neuron.
When we choose to move our arm for instance, neurons begin firing in our brain (our cerebrum), it sends the signal down to the thalamus, connects it to the cerebellum as well as through the brain stem, and the spinal chord. The path the neuron takes fallows the same pathway (and thus connects up to them) as other unconscious pathways. Neurons fire through the spinal chord, and eventually out to the arm. Then the reverse happens, messages from the arm fire immediately back up to the brain and eventually the cerebrum (but also to the cerebellum), and you're brain processes the new information (such as where you're appendages are in space, how balanced you are, exc... exc...) so it can send out more messages.
But how do we direct fine motor control? We can't on our own awareness. We can give general directions, but we don't have the capacity to consciously move only certain muscles, in an exact way. It's just too much information for our conscious brain to think of. This is why when we choose to begin a movement, the pathway those neurons take are also intervened by neurons from the cerebellum, and neurons from the eyes, and neurons from the inner ear... We initiated the neuron to fire, but the "auto-pilot" took care of the rest, and fine-tuned our movement (even if it hadn't done this movement before), shutting off the movement of some muscles, lessening the movement of others, making sure muscles are used that we keep our balance, exc... exc...
Sorry ramble so much :/, to answer "how do we start a movement?" is a surprisingly complicated topic...