The words good and well have been in English since its earliest incarnation.
When Beowulf finds the ancient sword in the underwater cave of Grendel’s mother, one of the words used to describe it is good.
Likewise, when the Beowulf poet contemplates the afterlife, he says, “Well [i.e., “in a state of good fortune”] is the person who after death seeks the Lord.”
Entries for both words in the Oxford English Dictionary are extremely long, encompassing numerous shades of meaning, many of them now obsolete.
Both words can function adverbially, but the use of good as an outright adverb declined in British English in the seventeenth century. It resurfaced in the nineteenth century as an Americanism, as noted in Bartlett’s American Dictionary (1859):
English travellers have repeatedly noticed the adverbial use of this word [good]. ‘He cannot read good.’ ‘It does not shoot good.’
Careful twenty-first century speakers and writers—Americans included—take care to avoid using good as an adverb in formal speech and writing, but colloquially (and in writing about sports), good is frequently used in place of well to modify a verb:
Nonstandard: We did pretty good sticking to our dinner plan this week except for one evening. (charlotteobserver.com)
Preferred: We did pretty well sticking to our dinner plan this week except for one evening.
Nonstandard: It doesn’t matter how good you played or how bad you played, did you win or not? (dailyherald.com)
Preferred: It doesn’t matter how well you played or how badly you played, did you win or not?
Nonstandard: He played good the first half of the bowl game, but he didn’t in the second half. (tennesean.com)
Preferred: He played well the first half of the bowl game, but he didn’t in the second half.
Nonstandard: Craig Anderson played great in net and the defense played good all the way out. (newsobserver.com)
Preferred: Craig Anderson played extremely well in net and the defense played well all the way out.
Apart from the clear situation in which well is preferable to good when modifying a finite verb, idiomatic uses exist in which good can be used adverbially without incurring disdain.
Idioms with good that function adverbially:
as good as
He as good as admitted that he was lying.
(“virtually, practically, in effect”)
good and
The principal was good and mad.
(“very, entirely”)
good-paying
Some speakers, knowing that we mustn’t say that a job “pays good,” go out of their way to change the acceptable idiom “good-paying” to the odd-sounding “well-paying.”
Note this sentence from a site called “geteducated”:
With only a minimal amount of classes and no previous experience, you can land this well-paying job.
Seems to me the sentence would sound more “educated” this way:
With only a minimal number of classes and no previous experience, you can land this good-paying job.
a good many
We’ve been glorifying wealth as the road to happiness for a good many years now.
Merriam-Webster defines “a good many” as “a lot,” but in the phrase, good modifies the adjective many—ergo, it’s being used adverbially.
