How is the perfect passive participle formed and used in Latin?

The perfect passive participle is found in the fourth column of principal parts tables. It is formed differently in each conjugation:

First: -atus (amatus)

Second: -itus/irregular (monitus)

Third: mostly irregular

Fourth: -itus (auditus)

Those parts that are irregular must be learned through principal parts tables. All parts are declined like a 1st/2nd declension adjective.

When translating a perfect passive participle, we must bear in mind its tense and voice. It is a prior action and passive. Therefore it is translated literally as 'having been'.

The participle always agrees in case, gender and number with the noun it is describing.

Eg.

urbem captam incenderunt - they burned the having-been-captured city

Or:

they burned the city that had been captured

Or better:

they captured and burned the city

The PPP can also be used as part of an ablative absolute.

The ablative absolute usually has a noun and participle agreeing in number and gender in the ablative case.

It is translated literally as 'with the NOUN having been VERB-ed,...'

Eg. urbe capta, rex discessit.

With the city having been captured, the king left.

This can be improved in a number of ways depending on the sense:

After he captured the city, the king...

When/since he captured the city, the king...

Having captured the city, the king...

In order to determine the best translation of an ablative absolute, you must look to the context within the sentence/passage.