Στειρώνω τη γάτα.

Modern Greek often drops the subject pronoun because the verb ending already tells you who is doing the action.

Here, στειρώνω ends in -ω, which marks first person singular: I.

So Στειρώνω τη γάτα is perfectly normal without εγώ.
If you want emphasis, you can say Εγώ στειρώνω τη γάτα.

στειρώνω is:

• present tense
• active voice
• first person singular
• imperfective aspect

So it is the form meaning I ...

Also, in Modern Greek, the dictionary form of a verb is usually this first-person singular present form, so you will often see verbs listed this way.

It can mean either, depending on context.

The Greek present tense can be used for:

• a general/habitual action: I spay/neuter the cat
• an action happening now: I am spaying/neutering the cat

If the speaker wants to make right now clearer, they can add something like τώρα:
Τώρα στειρώνω τη γάτα.

Because γάτα is the direct object here, not the subject.

• η γάτα = the cat as the subject
• τη γάτα = the cat as the object

So Greek uses the accusative feminine singular article here: τη(ν).

The feminine accusative article can appear as τη or την.

In standard modern usage, the final -ν is often dropped before many consonants. Since γάτα begins with γ, τη γάτα is the normal form here.

You may still see την in some writing or hear speakers who keep the -ν more often, but τη γάτα is completely standard.

Because many feminine nouns ending in -α have the same form in the nominative and accusative singular.

So:

• η γάτα = the cat, as subject
• τη γάτα = the cat, as object

The article shows the case change more clearly than the noun does.

Γάτα is a grammatically feminine noun.

That does not always have to match biological sex exactly. In everyday language, γάτα can be used generically for a cat, but Greek also has γάτος for a male cat.

So in this sentence, the grammar is feminine because the noun used is γάτα.

Because in Modern Greek, the letter combination ει is pronounced /i/.

So στει- sounds like sti-, not like English stei.

This is very common in Greek: several different spellings now represent the sound /i/, including:

• ι
• η
• υ
• ει
• οι
• υι

This is due to historical sound changes in the language.

A rough pronunciation is:

sti-RÓ-no ti GHA-ta

More accurately in IPA:

/stiˈrono ti ˈɣata/

A few useful points:

• Στ = st
• ει = i
• the stress is on ρώ
• γ before α is not a hard English g; it is a softer sound, roughly gh /ɣ/

Yes. Greek word order is more flexible than English word order.

Στειρώνω τη γάτα is a normal, neutral way to say it.

But Greek can move words around for emphasis or focus, for example:

• Τη γάτα στειρώνω — puts more focus on the cat
• Εγώ στειρώνω τη γάτα — emphasizes I

Even though the order can change, the article and verb endings still help show who is doing what.