Learn German: Der Zug fährt schnell. - The train is going fast.

The base verb is fahren (to travel or drive). It is a strong verb, which means it changes its vowel in the du (you) and er/sie/es (he/she/it) forms in the present tense. Because der Zug (the train) acts as a third-person "it", the 'a' changes to an 'ä', making the correct form fährt.

Why do we use fährt for a train "going"? Couldn't we use geht?

In German, the verb gehen (to go) is mostly used to mean going on foot or walking. When you are talking about a vehicle moving, or a person traveling by vehicle, you must use fahren.

The English translation says "is going". Why isn't there a word for "is" in the German sentence?

German doesn't have a separate "-ing" tense (like "is going" or "are driving") to show that an action is happening right now. The single present tense verb fährt covers both "goes" and "is going" in English.

Does the word schnell need a special ending here to match the masculine subject der Zug?

No, because here schnell (fast) is describing how the train travels, which makes it an adverb modifying the verb fährt. In German, adverbs never change their endings; they always stay in their basic dictionary form.