This homophonic pair (words that sound similar but have different spellings or meanings) is a common source of confusion for countless writers.
Phase is commonly used as a noun, meaning “a particular appearance or state in a regularly recurring cycle of changes.”
Example: I love to look up at the sky every night and observe the phases of the moon.
In verb form, phase is often paired with the words in or out, meaning “to adjust so as to be in a synchronized condition.”
Example: Next week, we are going to phase out the current process and phase in the new workflow system.
Faze is a verb meaning “to disturb the composure of.” It's often used in a negative construction.
Example: Nothing the scientist's critics said about his research seemed to faze him.
Another common form is the adjective unfazed, meaning "undaunted."
Example: She kept a straight face, unfazed by her friend's ridiculous excuses.
Still unsure about how to keep these words straight in your mind? Here's a fun little trick: think of the "z" in faze like the slash of Zorro's sword. Like the mark, this word is "cutting" and daunting in its usage.
Sources:
Webster's Third New International Dictionary, Unabridged, s.v. “faze,” accessed May 20, 2019, http://unabridged.merriam-webster.com.
Webster's Third New International Dictionary, Unabridged, s.v. “phase,” accessed May 20, 2019, http://unabridged.merriam-webster.com.
Webster's Third New International Dictionary, Unabridged, s.v. “unfazed,” accessed May 20, 2019, http://unabridged.merriam-webster.com.