Learn Hardcore Finnish: Tämä muistilappu on pöydällä.

tämä = this (near me)
tuo = that (over there) (not near the speaker, possibly nearer the listener or just further away)
se = it / that (already known from context, not strongly pointing at physical distance)

So:

Tämä muistilappu on pöydällä. = This note (right here) is on the table.
Tuo muistilappu on pöydällä. = That note (over there) is on the table.
Se muistilappu on pöydällä. = That note / The note is on the table (one we have been talking about).

Why is muistilappu written as one word and not as two words?

Finnish typically writes compound nouns as one word, not with spaces.

Muistilappu is made of:

muisti = memory
lappu = small piece of paper, slip

Together muistilappu = a reminder note / memo / sticky note.

If you wrote them separately (muisti lappu), it would look like two unrelated words, not a single concept.

What form is muistilappu in, and why does it look like that?

Muistilappu here is in the nominative singular form, which is the basic dictionary form.

Reasons:

It’s the subject of the sentence: This note is on the table.
Subjects in basic sentences are usually in the nominative: muistilappu (not muistilapun, etc.).

If you changed the role, you’d change the form, for example:

näen muistilapun = I see the note (object → partitive/genitive depending on context).

Why is there no word for a or the in this sentence?

Finnish has no articles like a / an / the.

The phrase Tämä muistilappu can be translated depending on context as:

this note
this memo
this (particular) piece of paper

Definiteness (a vs the) is shown by:

context
demonstratives like tämä, tuo, se
word order
rather than by separate words like a or the.

What case is pöydällä, and what does the ending -llä mean?

Pöydällä is in the adessive case.

Basic form: pöytä = table
Adessive: pöydällä = on the table / at the table

The ending -lla / -llä (choice of a/ä depends on vowel harmony) often expresses:

on a surface: pöydällä = on the table
at / by / on a place: asemalla = at the station
sometimes with / having (in a different structure, e.g. Minulla on... = I have...)

Here, it clearly means on top of the table.

What is the difference between pöydällä, pöydässä, pöydälle, and pöydältä?

All forms are based on pöytä (table) but show different cases and spatial relations:

pöydällä (adessive) = on the table / at the table
- static location on a surface
pöydässä (inessive) = in the table / inside the table
- used if something is literally inside a hollow table or compartment
pöydälle (allative) = onto the table / to the table
- movement onto a surface:
  - Laitan kirjan pöydälle. = I put the book onto the table.
pöydältä (ablative) = off (from) the table
- movement off a surface:
  - Otan kirjan pöydältä. = I take the book from the table.

In Tämä muistilappu on pöydällä, we use the static on the table form.

Could the word order be Pöydällä on tämä muistilappu instead? Does it change the meaning?

Yes, you can say:

Tämä muistilappu on pöydällä.
Pöydällä on tämä muistilappu.

Both are grammatically correct.

The difference is in emphasis / focus:

Tämä muistilappu on pöydällä.
- Focus on this note: This note (as opposed to another one) is on the table.
Pöydällä on tämä muistilappu.
- Focus on what is on the table: On the table, there is this note.
- Closer to an English there is sentence.

So word order in Finnish can shift what is being highlighted.

Is on a separate verb, and what form of the verb is it?

Yes, on is the verb here: it is the 3rd person singular present form of olla (to be).

The present tense of olla for singular:

minä olen = I am
sinä olet = you are
hän / se on = he / she / it is

So in Tämä muistilappu on pöydällä, the subject is Tämä muistilappu and on is is:

This note is on the table.

Could the sentence also mean There is a note on the table, or only This note is on the table?

With Tämä muistilappu on pöydällä, the most natural translation is This note is on the table, because tämä points to a specific note.

For a more neutral existential There is a note on the table, Finnish usually prefers:

Pöydällä on muistilappu. = There is a note on the table.

So:

Tämä muistilappu on pöydällä. → identifying a particular note
Pöydällä on muistilappu. → stating that some note exists on the table

Context can blur the difference a bit, but that’s the basic idea.

How would I say These notes are on the table using this sentence as a model?

You need to make both the demonstrative and the noun plural, and the verb must agree:

Nämä muistilaput ovat pöydällä.

Breakdown:

nämä = these
muistilaput = notes (plural nominative of muistilappu)
ovat = are (3rd person plural of olla)
pöydällä = on the table

So:

Tämä muistilappu on pöydällä. = This note is on the table.
Nämä muistilaput ovat pöydällä. = These notes are on the table.

Why don’t we need a separate word for it (like it is on the table)?

In this sentence, the subject is already expressed by Tämä muistilappu, so Finnish doesn’t add another it.

English:

This note, it is on the table. (would be redundant)

Finnish:

Tämä muistilappu on pöydällä.
- Tämä muistilappu = full subject
- on already agrees with it

Finnish does have se meaning it / that, but you only use it instead of the noun phrase, not in addition to it:

Se on pöydällä. = It is on the table.
not: Tämä muistilappu se on pöydällä in normal neutral speech.

What exactly does muistilappu mean—more like note, memo, or post-it?

Muistilappu literally is a small piece of paper used to remember something.

Depending on context, it can be translated as:

note
reminder note
memo
sticky note / Post-it (if the context is clear, like on a fridge or computer)

So in Tämä muistilappu on pöydällä, a natural translation is simply This note is on the table, but memo or reminder may also fit depending on the situation.