Learn Hardcore Japanese: tenin ha gaikokuzin ni kippu no kaikata wo setumeisuru to omoimasu. - I think the clerk will explain to the foreigner how to buy a ticket.

は marks 店員 (“clerk”) as the topic of the sentence—what the sentence is about. It doesn’t necessarily emphasize “the clerk” as the subject in a strictly grammatical sense (that would be が), but sets the stage: “As for the clerk….” If you said 店員が, you’d be introducing “the clerk” as a new or contrastive subject (“It’s the clerk who…”), whereas 店員は treats the clerk as already-on-the-table information or general topic.

Why is 外国人 followed by the particle に?

In Japanese, the person who receives an explanation is marked with に. Here 外国人に means “to foreigners.” The full pattern is AにBを説明する (“explain B to A”), so 外国人に切符の買い方を説明する = “explain how to buy tickets to foreigners.”

What function does 切符の買い方 serve, and how is it built?

切符の買い方 means “the way/method of buying tickets.” It’s built in two parts:

買い方 = verb stem + 方 (“–kō”), turning 買う (“to buy”) into the noun “(the) way of buying.”
切符の = genitive の, linking “ticket(s)” to “way of buying.”
So 切符の買い方 literally = “ticket(s)’ way of buying.”

Why is 切符の買い方 marked with を before 説明する?

Because 切符の買い方 is the direct object of 説明する (“to explain”). The construction is [Recipient]に[Content]を説明する. You use を on the thing being explained.

Why is 説明する in its dictionary/plain form before と思います rather than the polite 説明します?

When you use と思います (“I think…”) to quote a clause, that preceding clause must be in the plain form (dictionary or plain negative). So you say 説明すると思います, not 説明しますと思います. This is the standard “quotation” pattern: [plain-clause] と思う.

What nuance does ending with と思います add here?

と思います expresses the speaker’s conjecture or belief: “I think that…,” not a statement of certain fact. In this sentence it softens the assertion to “I imagine the clerk will explain how to buy tickets to foreigners,” implying some uncertainty.

Could you use 〜でしょう instead of 〜と思います, and what’s the difference?

Yes. でしょう also expresses speculation (“probably”).
• 説明するでしょう sounds a bit more detached or objective (“It will probably happen”).
• 説明すると思います is more personal (“I think it will happen”).
Both are common ways to soften a statement of future or conjecture.

What’s the difference between 説明する and 教える in this context?

Both can mean “to teach/explain,” but:

説明する focuses on providing a clear, detailed explanation or clarification of something.
教える is more general “to teach” or “to instruct” (you teach someone a skill or answer a question).
Here, 切符の買い方を説明する suggests walking someone through the steps; 切符の買い方を教える would also work but feels slightly more like “showing” or “teaching” rather than “explaining.”