Every main verb has two kinds of participles: a past participle and a present participle.
The past participle shows up in verb conjugation in two ways: (1) to form the perfect tenses with the auxiliary verb have (I have decided to retire) and (2) to form the passive voice with the auxiliary verb to be (The case was decided by the court). For regular verbs, the past participle is the same as the past tense, usually formed by adding ‑ed. For irregular verbs, you form the past participle in some other way; the past participle of drink, for example, is drunk. You can identify the past participle of a verb by completing this sentence: I have [insert verb here]. If you don't know the past participle for an irregular verb like swim, then check the dictionary.
The present participle shows up in verb conjugation in one way: It forms the progressive tense (also called the progressive aspect) with the auxiliary verb to be (He is preparing the report now). You form the present participle for all verbs by adding ‑ing. Sometimes you drop a silent -e, as in writing. And sometimes you double an ending consonant, as in occurring.
Finally, past and present participles appear in verbal phrases (the case decided by the court, the judge sitting next to the law clerk). They can also act as one-verb verbal adjectives (the exhausted runner, the smoking gun).