Learn Hardcore Finnish: Minä olen tosi väsynyt tänään.

This is a very typical neutral word order in Finnish: subject first, then verb, then descriptive parts, with time words often at the end or at the very beginning.

How do you conjugate olla (to be) in the present tense?

Olla is irregular in form but extremely common. Present tense:

minä olen = I am
sinä olet = you (singular) are
hän on = he / she is
me olemme = we are
te olette = you (plural / formal) are
he ovat = they are

In spoken Finnish you will often hear shortened forms:

mä oon, sä oot, se on, me ollaan, te ootte, ne on, etc.

But in your sentence olen is the standard written form.

What kind of word is tosi here, and how is it different from todella, erittäin, or hyvin?

Here tosi is an intensifier, like really / very in English.

Nuances:

tosi väsynyt – very common, slightly informal / colloquial;
similar to really tired.
todella väsynyt – a bit more neutral and standard, still everyday;
like really / truly tired.
erittäin väsynyt – more formal and stronger;
like extremely / very tired.
hyvin väsynyt – literally well tired, but idiomatically very tired;
more neutral / bookish than tosi.

So:

With friends: Olen tosi väsynyt tänään.
In something more formal: Olen hyvin / erittäin väsynyt tänään.

Is väsynyt an adjective or a verb form? How is it related to väsyä?

väsynyt is both:

grammatically it functions as an adjective: tired
historically it is the past participle of the verb väsyä (to get tired)

So:

väsyä = to get tired
väsynyt = (having) gotten tired → tired

In the sentence Minä olen tosi väsynyt tänään, väsynyt is a predicative adjective describing the subject minä.

You can also use it before nouns:

väsynyt ihminen = a tired person
väsynyt koira = a tired dog

Why does tänään end in -än? Is that a case ending?

tänään is an adverb meaning today, and it comes historically from the word tämä (this) plus a case ending.

Very simplified:

tämä päivä = this day
tänä päivänä = on this day (essive case: tänä)
Over time, tänä(ä)n contracted and fossilized into tänään = today

For a learner, you can just remember:

tänään = today
huomenna = tomorrow
eilen = yesterday

You do not need to decline tänään further; it is already in its fixed form.

Can I change the word order, like Tänään olen tosi väsynyt or Olen tänään tosi väsynyt?

Yes, Finnish word order is quite flexible. All of these are correct, with slightly different emphasis:

Minä olen tosi väsynyt tänään.
Neutral: I am really tired today.
Olen tosi väsynyt tänään.
Same meaning, without pronoun; very natural.
Olen tänään tosi väsynyt.
Slight focus on today, but still neutral.
Tänään olen tosi väsynyt.
Clear emphasis on today (as opposed to other days):
Today, I’m (the one who is) really tired.

The main rule: verb olen must stay in second position or close to it; the rest can often be reordered for emphasis.

How would you say this more informally, like in spoken Finnish between friends?

Common spoken-Finnish versions:

Mä oon tosi väsynyt tänään.
Oon tosi väsynyt tänään. (subject dropped)
Even more casual: Oon ihan sikan väsynyt tänään. (very colloquial, with extra slang intensifier)

Main spoken features:

minä → mä
olen → oon
Pronoun often dropped because oon already shows the person.

How do you pronounce the difficult vowels and double letters in this sentence?

Key points:

Vowel length matters (short vs. long):
- In tosi and väsynyt all vowels are short.
- In tänään, the ää is long: tä-nää-n.
  Do not say it like English tan-an; lengthen ää clearly.
Special vowels:
- ä: like a in cat, but held a bit clearer/purer.
  In minä, tänään, väsynyt.
- y: a front rounded vowel, somewhere between i and u.
  Try saying i with rounded lips: väsynyt ≈ vesynyt with rounded y.
Stress:
- Finnish always stresses the first syllable of a word:
  MInä OLen TOsi VÄSynyt TÄNään.

Aim for clear, even rhythm, without reducing unstressed vowels (unlike in English).

How do you make this sentence negative?

In Finnish, negation uses a separate verb ei plus the main verb in a special form.

Affirmative:

Minä olen tosi väsynyt tänään.

Negative:

Minä en ole tosi väsynyt tänään. = I am not really very tired today.

However, more natural with a weaker intensifier:

Minä en ole kovin väsynyt tänään. = I am not very tired today.

Patterns:

minä en ole = I am not
sinä et ole = you are not
hän ei ole = he / she is not
me emme ole = we are not
te ette ole = you (pl) are not
he eivät ole = they are not

Is there a difference between Minä olen tosi väsynyt tänään and Minua väsyttää tänään?

Yes, the structure and nuance differ:

Minä olen tosi väsynyt tänään.
Literally: I am really tired today.
- Describes your state with an adjective väsynyt.
Minua väsyttää tänään.
Literally: It tires me today, I feel sleepy / tired today.
- minua = me (in partitive case)
- väsyttää = an impersonal verb form to make (someone) tired
- Very idiomatic: I feel tired, often specifically sleepy.

Both are natural and close in meaning, but:

olen väsynyt = more like a description of your condition.
minua väsyttää = more like I feel tired / something makes me feel tired now.

Is tosi väsynyt too informal to use at work or in formal writing?

Context matters:

In everyday speech, even at work, tosi väsynyt is fine.
In formal writing (reports, official emails, academic texts), you would usually prefer more neutral intensifiers:
- Olen hyvin väsynyt tänään.
- Olen erittäin väsynyt tänään.

So:

Talking to colleagues or friends: Olen tosi väsynyt tänään. – OK.
Writing something official: prefer hyvin / erittäin väsynyt.