Learn Dutch: Wie gaat met de trein? - Who is going by train?

Just like in English, the question word wie (who) is treated as a singular word. Even if you expect the answer to be a group of people, you still ask the question using the singular form gaat (goes).

The translation says "by train", but doesn't met mean "with"?

Yes, met literally means "with". In Dutch, you don't travel "by" a vehicle, you travel "with" it. So, you say met de trein (with the train), met de fiets (with the bike), and so on.

Why is there a de before trein? In English we just say "by train".

In Dutch, when talking about modes of transportation, you usually need to include the article "the" (de or het). You cannot just say met trein. It always has to be met de trein (literally: with the train).

How do I know gaat means "is going" and not just "goes"?

Dutch generally uses the simple present tense for both situations. The single word gaat translates to both "goes" and "is going". You can tell which one makes sense based on the context of the conversation.