Learn Hardcore Chinese: lǎoshī xiān shuō yǔfǎ, ránhòu ràng wǒmen xiě jùzi. - The teacher first explains the grammar, then lets us write sentences.

先 goes before the first verb: 老师先说语法 – "The teacher first talks about grammar."
然后 goes before the second action: 然后让我们写句子 – "then has us write sentences."

So the pattern is:
A 先 + Verb 1 …，然后 + Verb 2 …
= First do A, then do B.

Can I use 再 instead of 然后, like 老师先说语法，再让我们写句子? Is there any difference?

You can say both:

老师先说语法，然后让我们写句子。
老师先说语法，再让我们写句子。

Both are natural and mean "The teacher first explains grammar, then has us write sentences."

Nuance (small, often ignored in everyday speech):

然后 is a bit more neutral and narrative ("and then…").
再 often gives more of a "next step" / "do this after that" feeling and is very common in instructions.

In a classroom routine, they’re both fine; many speakers use them almost interchangeably here.

How do we know this is in the past (like "the teacher first explained…") when there is no tense marker or past tense?

Chinese doesn’t mark tense (past/present/future) the same way English does. Instead, it relies on:

Context (what you’re talking about)
Time words (昨天, 刚才, 明天, etc.)
Aspect markers like 了, 过, 着 (to show completion, experience, ongoingness, etc.)

In 老师先说语法，然后让我们写句子。 there is no explicit tense. It could mean:

"The teacher first explains grammar, then has us write sentences." (a routine)
"The teacher first explained grammar, then had us write sentences." (a specific past class)

Which one is meant depends on the surrounding context, not on verb changes.

Why is there no 了 in this sentence? Would 老师先说了语法，然后让我们写了句子。 be better?

No 了 is needed here; the sentence is already complete and natural.

Without 了, it can describe a habitual sequence (what the teacher typically does in class).
With 了, it more strongly suggests a specific completed event.

More natural options for a single past event:

老师先讲了语法，然后让我们写句子。
(Focus on "taught/explained grammar" as a completed action.)
老师先讲语法，然后让我们写了句子。
(Focus on "had us write sentences" as completed.)

Putting 了 on both verbs (说了…写了…) often sounds a bit heavy or unnatural unless you really want to emphasize both completions.

What exactly does 让 mean here? Is it "let", "make", or "ask"?

In this sentence, 让 is a causative verb: "to have someone do something / to make someone do something / to let someone do something."

让我们写句子 literally: "cause us to write sentences."

Depending on context and tone, English might render it as:

"has us write sentences"
"asks us to write sentences"
"lets us write sentences"
sometimes just "we write sentences" (implicit causation)

Here, in a classroom routine, "has us write sentences" or "asks us to write sentences" fits best.

Why is the order 让我们写句子 and not 让我们句子写 or something else?

Chinese generally follows Subject – Verb – Object order.

In 让我们写句子:

让 = verb 1 ("cause/let")
我们 = object of 让 ("us")
写 = verb 2 ("write")
句子 = object of 写 ("sentences")

So the pattern is:

让 + [person] + [do something]
让我们写句子 = "have us write sentences."

A structure like 让我们句子写 breaks the usual Verb–Object pairing 写句子 and sounds ungrammatical.

"句子" is translated as "sentences" here. Why is there no plural marker? How do we know it’s plural?

Chinese nouns usually don’t change form for singular vs. plural:

句子 can mean "sentence" or "sentences", depending on context.

In 让我们写句子, you know it’s likely plural because:

我们 = "we" (a group), and
In class, if a teacher has the whole class write, it’s usually more than one sentence.

If you need to be explicit, you can add a measure word:

写一个句子 – "write one sentence"
写几个句子 – "write several sentences"
写很多句子 – "write many sentences"

Could we just say 老师先说语法，然后我们写句子。 without 让? What’s the difference in meaning?

Yes, 老师先说语法，然后我们写句子。 is grammatically fine and understandable.

Difference:

老师先说语法，然后让我们写句子。
Emphasizes that the teacher initiates/assigns the action: "then has us write sentences."
老师先说语法，然后我们写句子。
Just states the sequence: "then we write sentences," without explicitly saying the teacher made us.

In a classroom context, 让我们写句子 sounds more like describing the teacher’s teaching procedure or instructions.

Why use 说语法? Could we also say 讲语法 or 教语法? Are they different?

All are possible but slightly different:

说语法 – literally "talk about grammar."
Broad; could be just mentioning or explaining grammar points.
讲语法 – "explain/talk through grammar."
Very common in a classroom sense: the teacher explains grammar.
教语法 – "teach grammar."
Emphasizes teaching as a subject (grammar as course content).

In a typical classroom description, many speakers might naturally say:

老师先讲语法，然后让我们写句子。

But 说语法 isn’t wrong; it’s just slightly more general/colloquial.

Why is there no 是 (like 老师是先说语法…)? In English we might be tempted to say "The teacher is first…"

In Chinese, 是 is not used before adverbs like 先 in this way.

The structure is simply: Subject + (time/sequence adverb) + Verb.
So: 老师先说语法 (Teacher first talks about grammar), not 老师是先说语法.

You would use 是 if you are making a contrastive "it is … that …" structure:

老师是先说语法，然后才让我们写句子。
"It’s that the teacher first explains grammar, and only then has us write sentences."
(Emphasis on 先说语法 vs. some other order.)

Without that special emphasis, you just leave 是 out.

Where can 先 go in the sentence? Could we put it somewhere else?

In this kind of sentence, 先 is an adverb of sequence and normally goes right before the verb it modifies:

老师先说语法 – correct.
先老师说语法 – wrong (unless 先老师 is some special phrase, which it isn’t here).
老师说先语法 – wrong.

General pattern:

Subject + 先 + Verb + (Object)
老师先说语法
我们先写句子

So 先 should sit directly before the first action’s verb.

Is the comma ， important here? Does it mean anything special grammatically?

The comma ， simply separates the two clauses:

老师先说语法，
然后让我们写句子。

It doesn’t add extra grammar meaning; it just reflects the pause you naturally make when saying "First X, then Y."

In writing, you almost always use some punctuation (comma or a slight pause) between two independent clauses like this, especially when linked by 然后/再.