Learn Hardcore Japanese: asita ha tomodati no hi{kosi no tetudai wo simasu. - I will help with my friend's move tomorrow.

は marks the topic: “As for tomorrow, …” It’s common to topicalize time expressions.
に marks a specific point in time, but with relative days like 今日/明日/昨日, に is normally omitted. So 明日(に)します → the に is usually dropped.
You can say 明日には… to add contrast/emphasis (“at least/by tomorrow, …”). Plain 明日に… is generally unnatural in this sentence.

How is the chunk 友達の引っ越しの手伝い structured?

It’s a nested “of” chain with の:

友達の引っ越し = “my friend’s move”
(友達の引っ越し) の手伝い = “help with (my friend’s move)” So the whole thing means “help with my friend’s move.”

Which is more natural here: 手伝いをします or 手伝います?

Both are correct. In everyday speech, many would say the verb:

明日は友達の引っ越しを手伝います。 (concise and common) The noun + する is also fine:
明日は友達の引っ越しの手伝いをします。 Nuance: the verb form feels a bit more direct; the noun form can sound slightly more formal or matter-of-fact.

Can I replace 手伝う with 助ける?

Generally no.

手伝う = help/assist with a task (appropriate for moving).
助ける = save/rescue someone from danger or a serious problem.
Use 手伝う for chores, work, moving, homework, etc.

Is it okay to have two の in a row like 友達の引っ越しの手伝い?

Yes. Japanese commonly chains の for possession/attribution. Two or even three are fine. If the chain gets long and heavy, consider rephrasing.

How do I read the key words, and are there different readings for 明日?

明日: あした (everyday), あす (somewhat formal, news), みょうにち (very formal/written).
友達 (or 友だち): ともだち.
引っ越し: ひっこし.

Where is “I” in this sentence?

It’s omitted because it’s clear from context. Japanese often drops the subject. If you need to state it, say:

私は明日、友達の引っ越しの手伝いをします。

Why does します (present tense) talk about the future?

Japanese doesn’t have a separate future tense. The non-past (〜する/〜します) covers present and future; time words like 明日 make it future. For a stronger “plan,” you can use 予定/つもり (see below).

Can I drop を in 手伝いをします?

With many する-compounds, を is optional (e.g., 勉強(を)します). For 手伝い:

お手伝いします is a very common set phrase (especially in customer service).
Plain 手伝いします sounds odd; keep を unless you add the polite お: 手伝いをします / お手伝いします.

Is 友達 singular or plural? And what about 友達 vs 友だち?

友達 can mean “friend” or “friends” depending on context; Japanese doesn’t mark plural by default.
The 達 here is part of the word and doesn’t automatically pluralize it.
友だち (with だち in kana) and 友達 (all-kanji) are both common spellings; no real difference in meaning.
More formal word for “friend” is 友人.

What’s the casual/plain version?

Polite: 明日は友達の引っ越しの手伝いをします。
Plain: 明日は友達の引っ越しの手伝いをする。
Very natural alternative with the verb: 明日は友達の引っ越しを手伝う。

How can I state it as a plan or intention?

Plan/schedule: 明日は友達の引っ越しを手伝う予定です。
Intention: 明日は友達の引っ越しを手伝うつもりです。
It’s arranged/decided: 明日は友達の引っ越しを手伝うことになっています。

引っ越し vs 引っ越す vs 引っ越しをする — what’s the difference?

引っ越す is the verb “to move (house).” Polite: 引っ越します.
引っ越し is the noun “a move/moving.”
引っ越しをする / 引っ越しする also mean “to move.” All are common; 引っ越す is the straightforward verb form.

Why is there a small っ in 引っ越し?

The small っ indicates a brief stop and doubles the following consonant (gemination).

Pronounce ひっこし (not ひこし).
It affects rhythm and can change meanings in other words, so it matters.

Are spaces normal in Japanese writing?

No. Native writing doesn’t use spaces between words. They’re added here for learners. A native-style sentence would be:

明日は友達の引っ越しの手伝いをします。

Can I reorder parts of the sentence?

Yes, for emphasis:

明日は友達の引っ越しを手伝います。 (very common)
友達の引っ越しの手伝いは明日します。 (“As for helping with my friend’s move, I’ll do it tomorrow.”) All are grammatical; choose based on what you want to highlight.

How do I say “go help my friend move”?

Use 〜に to mark purpose:

明日は友達の引っ越しを手伝いに行きます。 = “I’m going to go help with my friend’s move.”

When should I use お手伝い?

The お adds politeness. お手伝いします is common when speaking to customers/clients or being very polite:

店員: 何かお手伝いしましょうか。 (“May I help you with something?”) With a friend, plain 手伝う/手伝います is more natural.

Could I say 明日が… here?

Not in this sentence. が marks the grammatical subject, and 明日 isn’t the subject of します. Use 明日は (topic) or just 明日、 to set the time.