For example: Sequoyah's system of writing was so simple that Cherokee children could learn to read in only a few weeks. "That Cherokee children could learn to read in only a few weeks" is the adverb clause, does it modify "so", "simple" or some other word?

Is there a way to figure out easily which word it modifies or do you just kinda "know"?

1) an adverb modifies another adverb or an adjective.

2) It would make sense that an adverb clause would modify another adverb, an adjective, or a verb.

3) "simple" seems to modify "writing", so "simple" would be an adjective.

4) I would go with the word "simple".

5) "So" is more of a conjunction or connecting word like "and, or, although, & but."

Since adverbs modify verbs, adverbs and adjectives, you have to look for one of them. Adverb clauses answer questions such as when, where, why, to what extent, etc. So "that Cherokee children could learn to read in only a few weeks" tells how simple his system was, therefore, it modifies simple.

adverbs modify verbs and adjectives (and possibly other adverbs). Think about what the clause is clarifying. What word is it clarifying (only picking out the verbs, adjectives and other adverbs): Sequoyah's, was, so, or simple?