These three words are easily confused, but it’s easy to sort out the confusion.
Conscious is an adjective meaning aware—either, as Samuel Johnson puts it, “Endowed with the power of knowing one’s own thoughts and actions,” or “having the knowledge of any thing without any new information.” “I am conscious of the pitfalls in writing about a controversy like that,” for example, would mean that I already know what the pitfalls are without anyone’s having to tell me.
Conscious is almost never a noun except as a technical term of Freudian psychology, where “the conscious” can mean “the self-aware mind,” as opposed to “the unconscious.”
Consciousness is the state of being conscious. “It was a while before women’s rights entered the public consciousness” means that it was a while before the public at large became aware of women’s rights as an issue.
Conscience is “the knowledge or faculty by which we judge the goodness or wickedness of ourselves,” again quoting Johnson. “My conscience is clear,” for example, means “I know I did nothing wrong.”
We often see conscious used incorrectly for either conscience or consciousness.
Wrong: He also added his conscious is clear. “I’d been in the village for 25 years, and I felt I did as much as I could for the county,” he said.
The local politician quoted here meant that his conscience is clear—unless he was using the Freudian technical term “conscious” as in “conscious mind,” in which case he means “I don’t have a thought in my brain.” We’ll let him pick which interpretation he likes best.
Wrong: The whole trilogy seemed to have evaporated from the public conscious.
The critic means that the trilogy evaporated from the public consciousness, meaning that the public is no longer aware of it.