Where should the commas in a sentence like below: She was usually a calm person but the dogs frightened her and she reacted by yelling.?

She was usually a calm person, but the dogs frightened her and she reacted by yelling.

One might mistakenly think a comma should go before "and." When "and" introduces a coordinate clause, grammar calls for a comma. However, in this instance, the clause after "and" isn't a coordinate clause but is a nominal clause in a list of two things that relate back to "but." That means that "and" isn't introducing a new main clause to the sentence but is instead introducing the final item in a list of two things being excepted. Granted, there is a grammatical convention for putting a comma before "and" when it introduces the last item of a list, sometimes referred to as an Oxford comma or serial comma, but that convention only applies when the list is of three or more things, not when it is of only two things.

Wherever you like. But one nice way to flow it might be.

She was usually a calm person, but the dogs frightened her and she reacted by yelling.

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I would punctuate it as follows:

"She was usually a calm person, but the dogs frightened her - and she reacted by yelling."

Before "but."

before every conjunction that separates 2 complete sentences

, but

, and

She was usually a calm person, but she yelled when the dogs frightened her