Learn Italian: Signore e signori, presentino il permesso all'ingresso. - Ladies and gentlemen, submit the permit at the entrance.

This is the formal plural command, used when addressing a group politely (the Loro form). For -are verbs like presentare (to submit or present), this formal plural command ends in -ino.

How would this command change if I were only talking to one person?

You would say presenti. When giving a formal command to just one person (the Lei form), -are verbs take an -i ending instead.

Wait, doesn't Signore mean 'Sir'? Why is it translated as 'Ladies'?

It can mean both depending on the context! Signore is the word for 'Sir', but it is also the plural form of Signora (Lady). In the standard greeting Signore e signori, it always means 'Ladies'.

Why does it say all'ingresso instead of just a ingresso?

In Italian, you must combine the preposition a (at) with the definite article. Since ingresso starts with a vowel, the article is l'. When you combine a + l', you get all'.