Το ξύλινο τραπέζι στο σαλόνι ταιριάζει με τον μπλε καναπέ.

Because τραπέζι is a neuter singular noun, and the adjective ξύλινο has to agree with it in gender, number, and case.

• το = the for a neuter singular noun
• ξύλινο = wooden in the neuter singular form
• τραπέζι = table

So:

• ο ξύλινος... would be masculine
• η ξύλινη... would be feminine
• το ξύλινο... is neuter

Greek adjectives usually change form to match the noun they describe.

Στο is the contracted form of σε το.

• σε = in, at, to
• το = the

So:

• στο σαλόνι = in the living room

This contraction is extremely common in Modern Greek:

• σε + το = στο
• σε + τη(ν) = στη(ν)

And σαλόνι is also a neuter noun, so it takes το.

Greek uses the definite article more regularly than English. In this sentence, each noun phrase has its own article:

• Το ξύλινο τραπέζι
• στο σαλόνι
• τον μπλε καναπέ

In English, you might sometimes omit an article, but in Greek it usually sounds more natural to include it when talking about a specific thing.

So Greek often says what feels more like:

• the wooden table
• the living room
• the blue sofa

rather than dropping the.

Because after με (with), Modern Greek uses the accusative case.

So:

• ο καναπές = the sofa
  nominative, used as the subject form
• τον καναπέ = the sofa
  accusative, used after με

That is why you get:

• με τον μπλε καναπέ = with the blue sofa

The noun changes from καναπές to καναπέ, and the article changes from ο to τον.

Good question. Μπλε is one of those adjectives that are usually indeclinable, meaning they do not change form.

So you can have:

• ο μπλε καναπές
• η μπλε καρέκλα
• το μπλε τραπέζι

The adjective μπλε stays μπλε no matter the gender or case.

That is different from adjectives like ξύλινος / ξύλινη / ξύλινο, which do change.

Ταιριάζει is the 3rd person singular present tense of the verb ταιριάζω.

Here it means:

• it matches
• it goes well with
• it suits

The subject is Το ξύλινο τραπέζι, which is singular, so the verb is singular too:

• Το τραπέζι ταιριάζει = The table matches

Some useful related forms:

• ταιριάζω = I match / I fit / I suit
• ταιριάζεις = you match
• ταιριάζει = he/she/it matches

In this sentence, the most natural reading is that στο σαλόνι goes with το ξύλινο τραπέζι:

• The wooden table in the living room matches the blue sofa.

So it sounds like the table is in the living room.

But Greek word order can sometimes leave a little room for interpretation, just like English can. If you wanted to make the location clearly relate to the whole situation, you might rephrase the sentence.

As written, most learners should understand στο σαλόνι as modifying τραπέζι.

Yes. Greek word order is more flexible than English because the endings and articles give grammatical information.

This sentence could be rearranged, for example, as:

• Στο σαλόνι, το ξύλινο τραπέζι ταιριάζει με τον μπλε καναπέ.

That version puts more emphasis on in the living room.

Even so, the original order is very natural and straightforward.

Because καναπές is a masculine noun whose nominative singular ends in -ς, but in the accusative singular that -ς disappears.

So:

• ο καναπές = nominative
• τον καναπέ = accusative

This is very common with many masculine nouns in Greek.

A rough pronunciation guide is:

To KSEE-lee-no tra-PE-zee sto sa-LO-nee te-ree-AH-zee me ton ble ka-na-PE

A few helpful notes:

• ξ sounds like ks
• τραπέζι has stress on πέ
• σαλόνι has stress on λό
• ταιριάζει has stress on ά
• καναπέ has stress on the last syllable

Greek stress matters, so it is worth noticing the accent marks.

Yes, very often. A common pattern is:

• ταιριάζω με + accusative = match / go well with

Examples:

• Το φόρεμα ταιριάζει με τα παπούτσια.
  The dress matches the shoes.
• Αυτό το χρώμα ταιριάζει με το δωμάτιο.
  This color matches the room.

So in your sentence:

• ταιριάζει με τον μπλε καναπέ = matches the blue sofa

That is a very natural Greek structure.