Learn Hardcore Japanese: densya ga kuru made, hoomu de matimasu. - I will wait on the platform until the train comes.

The particle が marks the subject in subordinate clauses like 電車が来るまで (“until the train comes”). Using は there (電車は来るまで) would turn “the train” into a topic and add a contrastive or thematic nuance, which isn’t needed when you simply want to say “until the train comes.”

What does 来るまで mean, and why is 来る in its dictionary form?

The construction ～まで means “until.” You attach まで to the dictionary form of a verb (here 来る) to express “up to the time when [verb] happens.” So 電車が来るまで literally means “up to the time the train comes.”

What role does the particle で play in ホームで待ちます?

The particle で indicates the location of an action. In ホームで待ちます, it tells us where the waiting takes place (“at the platform”). If you used に instead, it would imply existence or arrival rather than the location of an action, so ホームに待ちます would be incorrect.

Why is ホーム written in katakana?

ホーム is a loanword (wasei-eigo) from English “home” (referring to a train platform), so it’s conventionally written in katakana. You could also use the native term 乗り場 (のりば), but ホーム is very common in station signage and everyday speech.

Is the comma after まで necessary?

No. Japanese commas are optional and mainly reflect natural pauses in speech. Both of these are correct:

電車が来るまで、ホームで待ちます。
電車が来るまでホームで待ちます。

How would you say this sentence in casual (plain) form?

Replace the polite 待ちます with the plain 待つ. You can also drop the comma or even some particles in very casual speech:

電車が来るまでホームで待つ。
電車来るまでホームで待つ。

Could you use a different verb instead of 来る for “arrive”?

Yes. You can use 到着する (とうちゃくする), which means “to arrive” in a more formal register:

電車が到着するまでホームで待ちます。

Is 電車が来るまで considered a subordinate clause?

Yes. 電車が来るまで is a time clause (a subordinate clause) that modifies the main verb 待ちます. In Japanese, such subordinate clauses always come before the main clause without needing conjunctions like “that” or “when” as in English.