Learn Hardcore Finnish: Huomenna on pieni juoksukilpailu koulun pihalla. - Tomorrow there is a small running competition in the school yard.

On is the 3rd person singular form of the verb olla (to be), so it means is (or there is in this kind of sentence).
Finnish doesn’t need a separate word like there to say there is; the structure [place/time] + on + [thing] already expresses there is/are.
So Huomenna on pieni juoksukilpailu… literally feels like Tomorrow is a small running competition…, but it’s understood as There is a small running competition tomorrow…

Why does the sentence start with Huomenna? Could it go somewhere else?

Starting with Huomenna (tomorrow) highlights the time; it tells the listener that when the event happens is important.
You can change the word order, for example:

Pieni juoksukilpailu on huomenna koulun pihalla.
Koulun pihalla on huomenna pieni juoksukilpailu.
All are grammatically correct; the main difference is which part (time, place, or event) you emphasize first.

Why is there no word like a or the before pieni juoksukilpailu?

Finnish has no articles like a/an or the.
The noun phrase pieni juoksukilpailu can mean a small running competition or the small running competition, depending on context.
Definiteness (whether it’s a or the) is not marked grammatically; it is understood from the situation or previous conversation.

What exactly is juoksukilpailu, and why is it written as one word?

Juoksukilpailu is a compound noun: juoksu (running / run) + kilpailu (competition). Together they mean running competition / race.
In Finnish, compound nouns are usually written as one word, not separated: juoksukilpailu, not juoksu kilpailu.
Writing them as two words would be seen as incorrect or at least very odd.

What case is koulun, and what does it literally mean?

Koulun is the genitive singular of koulu (school).
The genitive with -n often corresponds to English of or the possessive ’s.
So koulun piha literally means the yard of the school or the school’s yard.

What case is pihalla, and what does the ending -lla mean?

Pihalla is in the adessive case: piha (yard) + -lla (on/at).
The adessive often expresses location on or at something (and also certain abstract uses).
Here koulun pihalla means in the school yard / at the school yard.

What is the difference between piha, pihalla, pihalle, and pihalta?

All are based on piha (yard):

piha – basic form (yard)
pihalla (adessive) – in the yard / at the yard (location)
pihalle (allative) – to the yard (movement towards the yard)
pihalta (ablative) – from the yard (movement away from the yard)

So koulun pihalla = in/at the school yard,
koulun pihalle = to the school yard,
koulun pihalta = from the school yard.

Why do we use pihalla instead of pihassa here? Don’t both mean “in the yard”?

Both pihalla (adessive) and pihassa (inessive) can be translated as in the yard, but they have different nuances.

pihalla is the usual, natural choice for yard, courtyard, open outdoor area.
pihassa would feel more like inside an enclosed area and is less typical with piha.
So native speakers almost always say koulun pihalla for in the school yard.

Why is pieni in the basic form? Shouldn’t it have some case ending?

Pieni is an adjective modifying juoksukilpailu, and adjectives usually agree with the noun in case and number.
Here juoksukilpailu is in the nominative singular (the basic form) because it’s the logical subject of the on-sentence.
So the adjective also stays nominative singular: pieni juoksukilpailu.
If it were plural partitive, for example, you would get pieniä juoksukilpailuja (small running competitions).

Could I say Huomenna on pieni juoksukilpailu koulussa instead? How would that change the meaning?

Huomenna on pieni juoksukilpailu koulussa is grammatically correct but slightly different in meaning.
Koulun pihalla focuses on the yard/outdoor area of the school; the event is outside.
Koulussa (inessive, in the school) suggests the event is inside the school building or just somewhere in the school, without focusing on the yard.

Can I change the word order to Pieni juoksukilpailu on huomenna koulun pihalla? Does it still sound natural?

Yes, Pieni juoksukilpailu on huomenna koulun pihalla is natural Finnish.
This order puts more emphasis on pieni juoksukilpailu (the event itself) as the topic.
All these are fine, just with slightly different emphasis:

Huomenna on pieni juoksukilpailu koulun pihalla. (time first)
Pieni juoksukilpailu on huomenna koulun pihalla. (event first)
Koulun pihalla on huomenna pieni juoksukilpailu. (place first)

Why does Finnish use on (present tense) for something happening tomorrow? Isn’t that future?

Finnish normally uses the present tense to talk about future events when the time is clear from context or from a time word like huomenna (tomorrow).
So Huomenna on pieni juoksukilpailu… naturally means There will be a small running competition tomorrow.
Finnish does not have a separate grammatical future tense like English does; context does the job.

How would I say There will be two small running competitions in the school yard tomorrow?

You can say: Huomenna koulun pihalla on kaksi pientä juoksukilpailua.
Breakdown:

Huomenna – tomorrow
koulun pihalla – in the school yard
on – there is/are
kaksi – two
pientä juoksukilpailua – small running competitions (partitive singular after a numeral)

What part of speech is Huomenna? Is it related to huominen?

Huomenna is an adverb meaning tomorrow (answering when?).
It is related to huominen (tomorrow as a noun/adjective, e.g. huominen päivä – tomorrow’s day).
You normally use Huomenna alone to say tomorrow in sentences like this.