Learn Hardcore Japanese: maitosi zinzya de onazi negai wo simasu. - Every year I make the same wish at a shrine.

Japanese frequently drops the subject (and even the object) when it’s obvious from context. In this sentence, the listener/reader understands who is doing the action—presumably the speaker—so you don’t need to explicitly say 私 or 僕. Omitted elements are common in Japanese to avoid redundancy.

How is 毎年 read and used? Does it need a particle?

Reading: Most native speakers say まいとし, though まいねん appears in casual speech.
Part of speech: It’s a “time noun” (時を表す名詞) that functions adverbially.
Particle: It doesn’t require one. Time expressions like 毎年, 昨日, 来週 can stand alone before the verb.
Placement: It typically goes at the very beginning (time-place-object-verb order), but you could also place it right before the verb if needed.

What does the particle で do in 神社で? Could I use に instead?

で marks the location where an action takes place. Here, you are performing the action (making a wish) at the shrine.
に would mark a point of arrival or existence, not the site of the action. If you said 神社に行く (“go to the shrine”), that makes sense with に because you’re indicating destination. But for “pray/make a wish at the shrine,” you need で.

What kind of word is 同じ, and how does it modify 願い?

同じ is a na-adjective (形容動詞).
When you use a na-adjective attributively (to directly modify a noun), you attach な, but in casual writing/speech the な often disappears in vertical spacing or lists. Formally you’d write 同じな願い (though actually the correct attributive form is just 同じ願い—同じ behaves a bit like an exception).
It means “the same,” so 同じ願い = “the same wish.”

What is the grammar behind 願いをします? Why not just 願う?

願いをする is a noun + をする construction, common with Sino-Japanese nouns: e.g. 勉強をする, 準備をする, 掃除をする.
You take the noun 願い and add をする to mean “to perform the act of wishing.”
願う is also a verb (“to wish for”), but 願いをする puts the emphasis on the act or ritual of making the wish, especially in contexts like visiting a shrine.

Why is the word order 毎年 → 神社で → 同じ願いを → します?

Japanese sentences generally follow:
1) Time expressions → 2) Place expressions → 3) Objects/manner → 4) Verb
This keeps the flow logical: when, where, what, then action. Changing the order can sound odd or emphatic, though native speakers do occasionally move elements for emphasis.

If I wanted to say “I go to the shrine every year to make the same wish,” how would I express “go” as well?

You can use the verb stem + に行く pattern:
毎年神社で同じ願いをしに行きます。
Breaking it down:

願いをし (the stem of 願いをする) + に marks purpose (“in order to…”)
行きます means “go.”
So literally “(I) go (there) to do the wish.”

What’s the difference in nuance between 願いをする, 願う, and 祈る?

願いをする: Emphasizes the act of making a wish, often in a ritual or formal setting (like at a shrine).
願う: “To wish for” or “to hope for” something, more about the desire itself.
祈る: “To pray,” with a stronger connotation of spirituality or asking for divine intervention. You’d often see 神に祈る.
All three can overlap, but 願いをする sits in the middle as a ritualistic “make a wish.”