Υποθέτω ότι είσαι πολύ κουρασμένος σήμερα.

Υποθέτω means I suppose, I assume, or sometimes I guess, depending on context.

In this sentence, it is:

• 1st person singular
• present tense
• from the verb υποθέτω = to suppose / assume

So Υποθέτω ότι... literally means I suppose that...

A native speaker might also use νομίζω in many similar situations, but υποθέτω can sound a bit more like making an assumption from the situation.

ότι means that and introduces the clause after Υποθέτω.

So:

• Υποθέτω = I suppose
• ότι είσαι πολύ κουρασμένος σήμερα = that you are very tired today

Together:

• Υποθέτω ότι είσαι πολύ κουρασμένος σήμερα.
• I suppose that you are very tired today.

In English, that is often optional, and in Greek it can sometimes be omitted too in casual speech, though keeping ότι is very standard and clear.

You may also hear πως instead of ότι in everyday Greek:

• Υποθέτω πως είσαι πολύ κουρασμένος σήμερα.

That means the same thing here.

είσαι is the 2nd person singular form of είμαι (to be), so it means you are.

Since the sentence is talking to one person, Greek uses:

• είμαι = I am
• είσαι = you are
• είναι = he/she/it is

So:

• είσαι πολύ κουρασμένος = you are very tired

If you were speaking to more than one person, you would use:

• είστε πολύ κουρασμένοι = you are very tired (plural / formal)

Greek often leaves out subject pronouns because the verb ending already shows who the subject is.

Here, είσαι already tells us the subject is you (singular), so εσύ is not necessary.

• είσαι πολύ κουρασμένος = you are very tired

You can add εσύ for emphasis or contrast:

• Υποθέτω ότι εσύ είσαι πολύ κουρασμένος σήμερα.

That would sound more like:

• I suppose you are very tired today
  with extra emphasis on you

But in a neutral sentence, Greek normally omits it.

κουρασμένος agrees with the person being described.

Here it is:

• masculine
• singular
• nominative form

It matches an understood you referring to one male person.

So:

• to a man: είσαι κουρασμένος
• to a woman: είσαι κουρασμένη

If you were talking to more than one person:

• masculine or mixed group: είστε κουρασμένοι
• all-female group: είστε κουρασμένες

So the ending changes according to gender and number.

Yes, in this sentence it functions as an adjective, meaning tired.

Historically, it comes from a participle-like form of the verb κουράζω (to tire), but for learners, the most useful thing is to treat it like an adjective that agrees in gender and number:

• κουρασμένος = tired (masculine singular)
• κουρασμένη = tired (feminine singular)
• κουρασμένοι / κουρασμένες = tired (plural)

In the sentence:

• είσαι πολύ κουρασμένος
• literally: you are very tired

This is a very common Greek structure: είμαι + adjective

πολύ here means very.

It comes before the adjective it modifies:

• πολύ κουρασμένος = very tired

So the structure is:

• είσαι κουρασμένος = you are tired
• είσαι πολύ κουρασμένος = you are very tired

A helpful thing to remember is that πολύ can mean either:

• very before adjectives/adverbs
• much / a lot in other contexts

Here it clearly means very.

Yes, Greek word order is fairly flexible.

The sentence as given:

• Υποθέτω ότι είσαι πολύ κουρασμένος σήμερα.

is a very natural way to say:

• I suppose you are very tired today.

But σήμερα can move depending on emphasis:

• Υποθέτω ότι σήμερα είσαι πολύ κουρασμένος.
• Σήμερα υποθέτω ότι είσαι πολύ κουρασμένος.

These are all possible, though they do not all sound equally neutral. The original version is smooth and ordinary.

In general, Greek often places time expressions like σήμερα in different spots more freely than English does.

Yes, sometimes.

You may hear:

• Υποθέτω είσαι πολύ κουρασμένος σήμερα.

In everyday speech, that can sound natural. However, learners are usually safer keeping ότι, because it makes the structure clearer.

So:

• Υποθέτω ότι είσαι πολύ κουρασμένος σήμερα. = fully standard and clear
• Υποθέτω είσαι πολύ κουρασμένος σήμερα. = possible, more conversational

You may also hear πως instead of ότι, as mentioned earlier.

Yes, υποθέτω is correct and natural, but many speakers might more often say νομίζω in everyday conversation.

Compare:

• Υποθέτω ότι είσαι πολύ κουρασμένος σήμερα.
• Νομίζω ότι είσαι πολύ κουρασμένος σήμερα.

Both are fine, but the nuance is a little different:

• υποθέτω = I assume / I suppose
• νομίζω = I think

So υποθέτω can sound a bit more like you are drawing a conclusion from what you see.

You would change κουρασμένος to the feminine form κουρασμένη.

So:

• Υποθέτω ότι είσαι πολύ κουρασμένη σήμερα.

Everything else stays the same.

That is because the adjective must agree with the person being described.

Then you would change είσαι to είστε, and the adjective would become plural.

Examples:

• to a mixed group or a group of men:
  Υποθέτω ότι είστε πολύ κουρασμένοι σήμερα.

• to a group of women:
  Υποθέτω ότι είστε πολύ κουρασμένες σήμερα.

Also, είστε is used for formal singular you.
In that case, the adjective usually agrees with the actual gender of the person:

• formal to one man:
  Υποθέτω ότι είστε πολύ κουρασμένος σήμερα.

• formal to one woman:
  Υποθέτω ότι είστε πολύ κουρασμένη σήμερα.

A rough pronunciation guide is:

ipó-theto óti íse polí kurasménos símera

More approximately by parts:

• Υποθέτω → ee-po-THEH-to
• ότι → OH-tee
• είσαι → EE-se
• πολύ → po-LEE
• κουρασμένος → koo-raz-MEH-nos
• σήμερα → SEE-me-ra

A few helpful notes:

• αι in είσαι is pronounced like e
• ου is pronounced like oo
• η, ι, υ, ει, οι often sound like ee in Modern Greek

More or less, yes.

The structure is:

• Υποθέτω = I suppose
• ότι = that
• είσαι = you are
• πολύ κουρασμένος = very tired
• σήμερα = today

So the literal order is:

• I suppose that you are very tired today

That makes this sentence fairly straightforward for English speakers, but the main Greek-specific points are:

• no pronoun εσύ is needed
• the adjective changes for gender/number
• word order is somewhat flexible
• ότι may be present or omitted depending on style