Learn Hardcore Russian: Сначала я пишу письмо, затем читаю книгу. - First I write a letter, then I read a book.

сначала means “first” or “at first” and introduces the initial action.
затем means “then” or “after that” and introduces the following action.
Together they explicitly mark the order in which events occur.

What’s the difference between затем and потом?

Both mean “then” or “afterwards,” but затем is slightly more formal or literary, while потом is more colloquial. You can replace one with the other in most contexts, e.g. Сначала я пишу письмо, потом читаю книгу.

Why is there a comma before затем?

Here you have two independent clauses: “я пишу письмо” and “читаю книгу.” A comma is required before затем (and other similar connectors) to separate those clauses.

Why is the pronoun я included? Can it be omitted?

Russian verbs carry person and number endings, so я (“I”) is grammatically optional: Сначала пишу письмо, затем читаю книгу is perfectly normal. Including я adds emphasis or clarity.

Why are the verbs in the present tense? Isn’t this describing something in the future?