The perfect tense is used to refer to actions which are perfect or complete, already done/occurred.
What is the principal part of a verb?
Verbs all have principal parts, we can think of these as the things we have to memorize in order to effective conjugate a verb. For example, laudō has four principal parts.
Present Active Indicative: laudō, I praise
Present Active Infinitive: laudāre, to praise
Perfect Active Indicative: laudāvī, I have praised
Perfect Passive Participle laudātum, praised, having been praised
The third and fourth principal parts tend to not follow any rules and have many variations. So get to memorizing.
To get the stem for the perfect active system, drop the final -ī. Below are the conjugations in the perfect active indicative for laudāvī and ēgī.
Present Active Indicative (have)
Singular
Plural
1st
laudāvī
laudāvimus
2nd
laudāvistī
laudāvistis
3rd
laudāvit
laudāvērunt
Singular
Plural
1st
ēgī
ēgimus
2nd
ēgistī
ēgistis
3rd
ēgit
ēgerunt
Pluperfect Active Indicative (had)
Singular
Plural
1st
laudāveram
laudāverāmus
2nd
laudāveras
laudāveratis
3rd
laudāverat
laudāverant
Singular
Plural
1st
ēgeram
ēgeramus
2nd
ēgeras
ēgeratis
3rd
ēgerat
ēgerant
We can see that the endings for the pluperfect are just the imperfect for sum/esse.
Future Perfect Active Indicative (shall have)
Singular
Plural
1st
laudāvero
laudāverimus
2nd
laudāveris
laudāveritis
3rd
laudāverit
laudāverint
Singular
Plural
1st
ēgero
ēgerimus
2nd
ēgeris
ēgeritis
3rd
ēgerit
ēgerint
Again, we can see that the endings for the future perfect are just the future for sum/esse. With the only exception being that erunt is now erint, likely owing to the fact that the present perfect has erunt has the 3rd person plural ending. (see here for esse conjugations: Esse, Sum, et Possum)
Perfect vs Imperfect
The core difference between the perfect and the imperfect is that, well, perfect (from the latin perfectum) refers to completed actions. We, in English, use “have” ,“had”, and “will have” to convey this sense of completion. Inversely, an imperfect action is ongoing in the past. In English, we often use “used to” for this sense of continuity. The pluperfect (from latin plūs quam perfectum more than perfect) describes an action done in the distant past with respect to the recent past. “You had studied so the exam last Friday went well”. The future perfect predicts or describes an act that will be done in the future with consequences for a point in the even more distant future. The present perfect can also serve as the simple past tense.