Learn Hardcore German: Auf dem Merkzettel steht: Heute mache ich nur eine Überstunde. - On the reminder note it says: Today I’m only doing one hour of overtime.

Dative for a location (where something is): auf dem Merkzettel = on the note
Accusative for motion/direction (where something is put): auf den Merkzettel = onto the note (as in I write it onto the note)

Here, it’s describing where the text is written, so it uses dative.

What exactly is a Merkzettel, and why is it dem?

Merkzettel means a memo, reminder note, or cheat sheet (depending on context). It’s grammatically masculine: der Merkzettel, so in dative singular it becomes dem Merkzettel.

Why does German use steht (stehen) for text? It literally means “to stand.”

German commonly uses stehen to mean to be written/printed (somewhere):

Auf dem Schild steht ... = The sign says ...
Im Brief steht ... = The letter says ...

It’s idiomatic: the words are “standing there” in written form.

Why is the verb steht so early in the sentence?

Because German main clauses follow the V2 rule: the finite verb is in second position.
Here, the first position is taken by the prepositional phrase Auf dem Merkzettel, so the verb comes next:

Auf dem Merkzettel (position 1)
steht (position 2)
the content (what is written)

What is the “subject” of steht here? It doesn’t look like a normal noun subject.

The “thing that stands (is written)” is the following content, effectively: Heute mache ich nur eine Überstunde.
German often lets a clause or quoted content function like a singular subject, so the verb is steht (singular). You can also think of an implied es (it), like: On the note it says: ...

Why is there a colon after steht:? Could it be written differently?

The colon introduces the exact wording that follows (like introducing a quote). Common alternatives are:

Auf dem Merkzettel steht: ... (colon + direct content)
Auf dem Merkzettel steht, dass ich heute nur eine Überstunde mache. (with dass, subordinate clause)
Auf dem Merkzettel steht: „Heute mache ich nur eine Überstunde.“ (with punctuation like a quotation)

Why is Heute capitalized? Is that because of the colon?

Heute is capitalized because it begins a new sentence (the text written on the note). After a colon, German often treats what follows as a new sentence if it’s a full sentence—so it starts with a capital letter.

In Heute mache ich nur eine Überstunde, why is mache in second position?

Again, the V2 rule for main clauses:

Heute is in position 1 (a time adverbial)
mache is the finite verb in position 2
ich comes after the verb

So it’s: Heute | mache | ich ...

Why does it say mache ich ...—isn’t that inverted word order?

It’s normal in German. When something other than the subject comes first (here Heute), the verb stays second and the subject follows the verb:

Ich mache heute ... (subject first)
Heute mache ich ... (time first → subject after the verb)

Why is it eine Überstunde (singular)? I often see Überstunden machen.

Both are possible:

Überstunden machen = to do overtime in general (often plural)
eine Überstunde machen = to do exactly one overtime hour (or one unit of overtime)

So eine makes it specific: just one.

What case is eine Überstunde, and why?

It’s accusative because it’s the direct object of machen in this idiom:

eine Überstunde machen (accusative object)

Also, Überstunde is feminine: die Überstunde, so accusative feminine singular is still eine Überstunde.

Where does nur belong, and does its position change the meaning?

nur usually goes right before what it limits. Here it limits the amount of overtime:

Heute mache ich nur eine Überstunde. = I’m doing only one hour of overtime today.

If you move nur, the focus can shift:

Heute mache ich eine Überstunde nur. (uncommon/awkward)
Nur heute mache ich eine Überstunde. = Only today I’m doing an overtime hour (today is what’s limited)