The past participle is a special form of a verb that is used in a variety of situations.
It is most often used when constructing certain tenses (perfect, past perfect, future 2, and passive), but can also be used as an an adjective to take the place of the usually much longer subordinate clause.
The past participle is used as an adjective in place of a subordinate clause when the action in the subordinate clause took place before the action in the main clause.
⇒ first action was cleaning.
⇒ second action is parking
More information here: Participles as Adjectives
ge + verb stem + -(e)t
Verbs ending in –ieren don't get the "ge-"
ge + verb stem + -en
Once you know what category the verb goes in, the construction follows the rules of that category.
Mixed verbs are those where the past participle is formed with simple past form of the verb:
ge + verb stem in simple past + -t
There's not general rule about which verbs use this irregular construction. You just have to learn them. But it usually goes pretty fast because the past participle is used a lot
Some have a vowel change when forming the past participle. It's usually words that have a vowel change in the simple present tense. Additionally, the letter combination "ei" almost always changes to "ie."
Verbs with a vowel change almost always end in "-en."
ge + verb stem with vowel change + -en
prefix + ge + verb stem + -t/-en
The past participle of the main verb stays the same (just the prefix added to the front).
construction without "ge-" at the beginning.
prefix + verb stem + -t/-en
The past participle of the main verb stays the same, just without the prefix "ge-"!
Independent from the prefix, the base of the past participle stays the same.
More info about separable and inseparable verbs: Compound Verbs