Quick answer
Здесь свобо́дно?
zdyes svabódna — the impersonal -о form, so it works for any seat
The options
Здесь свобо́дно?Is this free?
Э́то ме́сто свобо́дно?Is this seat free?
Мо́жно?May I? — with a gesture, completely sufficient
Здесь не за́нято?This isn’t taken, is it?
Мо́жно сесть?May I sit down?
Why свобо́дно
The neuter short form свобо́дно works impersonally — “is it free here” — so you do not need to know the gender of whatever you are sitting on. With ме́сто (neuter) it agrees anyway.
The answers
Свобо́дно or Да, пожа́луйста means yes. За́нято means taken. And in a long queue or a waiting room, Я занима́ла — “I was holding it” — means someone has left a coat on it and will be back.
What you hear back
Да, свобо́дно.Yes, it’s free.
За́нято, извини́те.Taken, sorry.
Пожа́луйста, сади́тесь.Please, take a seat.
Здесь челове́к.Someone’s sitting here.
Typical mistakes
Здесь свобо́дный?
Здесь свобо́дно?
The impersonal short form ends in -о.
Мо́жно сиде́ть?
Мо́жно сесть?
сесть is the act of sitting down.
Check yourself
Which is correct?
The impersonal neuter form.