Oggi faccio un’ora di straordinario, ma domani esco presto.

In Italian, fare straordinario is the normal way to say to do/work overtime.

So:

• faccio straordinario = I’m doing overtime / I work overtime
• faccio un’ora di straordinario = I’m doing an hour of overtime

This is one of those expressions where Italian uses fare in a way English does not. A literal word-for-word translation sounds odd in English, but it is completely natural in Italian.

This follows a very common Italian pattern:

• un’ora di lavoro = an hour of work
• due chili di pane = two kilos of bread
• un bicchiere d’acqua = a glass of water

So un’ora di straordinario literally means an hour of overtime.

The di connects the quantity/time expression (un’ora) to the thing being measured (straordinario).

Because ora is a feminine noun, so the full form is una ora. In Italian, una is commonly shortened before a vowel:

• una amica → un’amica
• una idea → un’idea
• una ora → un’ora

So un’ora is simply the elided form of una ora.

Because straordinario here is a masculine noun meaning overtime.

It originally comes from an adjective meaning extraordinary, but in this context it functions as a noun. That is why you say:

• lo straordinario
• un’ora di straordinario

Not straordinaria, because you are not describing ora with an adjective here. You are naming the thing: overtime.

Italian usually leaves out subject pronouns when they are not needed, because the verb ending already tells you who the subject is.

• faccio = I do
• esco = I go out / I leave

So io is optional. You would normally add io only for emphasis, contrast, or clarity:

• Io faccio un’ora di straordinario, ma tu no.
  I’m doing an hour of overtime, but you aren’t.

In your sentence, the subject is clear, so leaving out io sounds natural.

Because Italian often uses the present tense for future actions when the time is clear from context.

Here, domani already tells you the action is in the future, so esco is perfectly natural:

• Domani esco presto. = Tomorrow I’m leaving early.

This is very common, especially for plans, schedules, or near-future actions.

You could also say:

• Domani uscirò presto.

That uses the future tense and is also correct, but domani esco presto is very common in everyday speech.

The verb is uscire, which basically means to go out or to leave.

In a work-related sentence like this, esco presto usually means:

• I leave early
• literally, I go out early

Italian often uses uscire where English would naturally say leave.

Examples:

• Esco dall’ufficio alle sei. = I leave the office at six.
• Oggi esco tardi. = Today I’m leaving late.

Presto is an adverb here, meaning early. It describes how/when you leave.

So:

• esco presto = I leave early

Adverbs in Italian often come after the verb, so this word order is very natural.

Also, presto does not change form. It stays presto no matter who is doing the action.

Putting oggi and domani first highlights the contrast between the two days:

• Oggi faccio un’ora di straordinario,
• ma domani esco presto.

This is very natural in Italian and helps organize the sentence clearly.

You could move them, for example:

• Faccio un’ora di straordinario oggi, ma esco presto domani.

That is possible, but the original version sounds more balanced and emphasizes the contrast better.

Yes. Both are possible, but they say slightly different things.

• Faccio straordinario = I’m doing overtime
• Faccio un’ora di straordinario = I’m doing an hour of overtime

The version with un’ora di is more specific because it tells you the amount of overtime.

You may also hear:

• fare degli straordinari = to do some overtime / overtime shifts
• fare ore di straordinario = to do hours of overtime

Ma means but and introduces a contrast.

Here the contrast is:

• today: extra work
• tomorrow: leaving early

So ma connects two opposite or contrasting ideas, just like but in English.

It is one of the most common conjunctions in Italian.