Learn Hardcore Japanese: watasi ha kuukou de okane wo ryougaesimasu.

は: topic marker (“as for me…”). It sets the context, not the grammatical subject per se.
で: place-of-action marker; where the action happens (at the airport).
を: direct object marker; marks what is being acted upon (money).

Can I use に instead of で after 空港?

空港で means “at the airport” (location of the action). This is correct here.
空港に is for existence or destination (“at the airport” in a static sense, or “to the airport”).
You might say: 空港に行ってお金を両替します (“I’ll go to the airport and exchange money”), but not “空港にお金を両替します.”

Can I drop 私 or お金?

Dropping 私 is very common when it’s obvious who the subject is: 空港でお金を両替します.
You can also drop お金 because it’s implied by 両替: 空港で両替します is perfectly natural.
Dropping both: 空港で両替します is often what you’ll hear.

Why is it します instead of する?

します is the polite form; する is plain/casual. Use します with strangers, service staff, coworkers, etc.
Plain: 空港で（お金を）両替する。
Polite: 空港で（お金を）両替します。

Is this present or future?

Japanese “non-past” (します) can mean present or future. Context decides:

Now/regularly: 今、空港で両替します。
Future/plan: 明日、空港で両替します。 Add a time word if you need to disambiguate.

Is 両替する one verb or a noun plus する?

It’s a “suru-verb”: 両替 (a noun, “money exchange”) + する (“to do”).
So:

（お金を）両替する／両替します = to exchange money
You can also say お金の両替をします (do the exchange of money).

How do I say “exchange dollars to yen”?

Use the pattern XをYに両替する:

空港でドルを円に両替します。 You can replace currencies as needed: ユーロを円に, 円をドルに, etc.

Can I change the word order?

Yes, elements before the verb are flexible, but the verb stays at the end.

空港でお金を両替します。 (neutral)
お金を空港で両替します。 (focuses first on “money”) Time expressions typically come early: 明日、空港でお金を両替します。

Why is there お before お金? Can I just say 金?

お金 is the normal, polite everyday word for “money.” The お is an honorific/politeness prefix that softens the word.
金 (かね) without お sounds blunt/rough; acceptable among close friends but not recommended broadly.
金を両替します is grammatically fine but can feel curt. Stick with お金 in neutral/polite speech.

What are natural ways to ask for/explain this at an airport?

両替できますか。 (Can I exchange money?)
両替をお願いできますか。 (Could you do a money exchange for me?)
両替所はどこですか。 (Where is the currency exchange counter?)
ドルを円に両替したいです。 (I’d like to exchange dollars to yen.) Adding すみません at the start makes it more polite.

What’s the difference between 両替する, 交換する, 換金する, and 替える/換える/変える?

両替する: exchange currencies (default verb for money exchange).
交換する: swap/exchange items with someone (not used for currency exchange).
換金する: convert assets to cash (e.g., traveler’s checks, gift cards).
替える／換える: to replace/exchange one thing for another; with money, you’ll see phrases like 外貨を円に替える.
変える: change/alter (state or plan), not typically used for currency exchange.

How do I make it past, negative, or a polite request?

Past (polite): 両替しました。
Negative (polite): 両替しません。
Past negative (polite): 両替しませんでした。
Plain past: 両替した。 / Plain negative: 両替しない。
Yes/no question: 両替しますか。
Polite request: 両替していただけますか。 / 両替してもらえますか。 / 両替してください。

Does で ever mean “by means of”? Could 空港で be misread that way?

で can mean “by means of” (e.g., バスで = by bus), but here it clearly marks place of action: 空港で = at the airport. It can’t mean “by airport” in this sentence.

How do I include amounts and be specific?

空港で300ドルを円に両替します。 (I’ll exchange 300 dollars to yen at the airport.)
You can add “into small bills/coins”: 小銭に両替します, 千円札に両替します.
With fees: 手数料はかかりますか。 (Is there a fee?)

Can I use 僕 or 俺 instead of 私?

私（わたし）: neutral/polite; used by anyone; safest choice.
僕: common casual male first-person; polite enough in many settings.
俺: very casual/masculine; avoid in polite or formal contexts.