Okay, you have remember that infinitives are actually nouns (a strange kind of noun but still, a noun), connected to the world of verbs. Well, participles are actually adjectives, but they are connected to the world of verbs. What does that mean? It means that a participle has gender, number, and case, just like an adjective, but it also has tense (present, perfect, future) and voice (active, passive), just like a verb.
Here is a chart showing the types of Latin participles, using the verb "tego":
Notice that this chart is out of balance: there is not a present passive participle, and there is not a perfect (past) active participle. English is out of balance in pretty much the same way, though, so this does not feel too strange for us. Like Latin, English has a present active participle (covering) and a past passive participle (covered).
Present Active Participle. The present active participle is formed from the first and second principal parts of the verb: for the first conjugation, it ends in -ans; for second conjugation, it ends in -ens; for third conjugation, it ends in -iens or -ens; and for fourth conjugation, it ends in -iens. The participle is a third declension adjective, with a genitive singular form in -ntis.
Perfect Passive Participle. The perfect passive participle is the fourth principal part of the verb. It is a regular first-second declension adjective.
Future Active Participle. The future active participle is formed from the fourth principal part of the verb; simply replace the final -us with -urus. This participle is also a regular first-second declension adjective.
Future Passive Participle. The future passive participle is most easily formed from the present participle; simply replace the final -ns with -ndus. This participle is also a regular first-second declension adjective. It has a special connotation of obligation or necessity: Carthago delenda est, Carthage must be destroyed! Or, to keep on with the theme of tego: Carthago tegenda est, Carthage must be covered!