Adapt: to use something in a new way or do things in a new way; to make more suitable or functionable.
Adopt: to make something your own, such as a child, belief, or habit.
Adept: skilled or talented at a particular task or skill.
A Closer Look
These are three completely different words, although their related meanings may add to your confusion. Adapt and adopt are verbs. Adapt means “to use something in a new way” or “do things in a new way” and adopt means “to make something your own”, such as a child, belief, or habit. These words have a variety of rather distinct uses within these meanings:
Adapt
a. We can adapt this rock to use it as a table.
b. People are always adapting the play Hamlet in new ways.
c. When you move to a new country, you need to adapt (to new ways).
d. According to the theory of evolution, species change their forms in order to adapt to pressures in their environments.
Adopt
a. She adopted a child because she could not have one.
b. People are adopting veganism in order to reduce climate change.
c. I cannot adopt that attitude because it is narrow-minded.
As you can see, the meanings of adapt and adopt do overlap (in (a) and (b) above), but still differ. It may help to remember two words: adaptation is what species do in evolution; adoption is when you become the new legal parent of a child.
Adept
Adept is not a verb; it is an adjective meaning “skilled or talented” at something in particular, not just in general:
Correct: She was quite adept at writing.
Incorrect: *She was so adept that she got into Mensa.
It can also be used as a noun referring to a master of anything:
He is an adept at software engineering.
Adept also has an old-fashioned meaning, of “a magician”:
The adept drew a diagram on the floor and began chanting spells.
The opposite of adept (as an adjective) is inept; this may help you remember adept:
The inept manager angered the office employees.
The audience walked out of what was clearly an inept stage performance.