Verbs have different forms depending on how we talk about them. See here for a refresher on verb tenses.

Simple Past Tense is pretty straight forward; we use past tense to talk about shit that happened in the past.

I killed someone last night.

She killed everyone last night.

Participles are a little trickier.

What is a Participle?

A participle is the verb form that can also act as an adjective (e.g., the running water). Participles are also paired with other words, such as have or has, to form verb tenses.

Past Participle is used to talk about completed (perfect) actions.

I have killed people.

She has killed people.

Present Participle is used to talk about ongoing (continuous) actions. This is the ing form of the verb.

I am killing.

She is killing.

How to Form the Past Tense and Past Participle

For regular verbs, the past tense and past participle are usually formed by adding -ed at the end of the root verb form (or just -d if the word already ends in -e).

Kill → Killed
Die → Died

However, some verbs are assholes and require a little more work.

1. If the verb ends in a consonant preceded by a single vowel (e.g., rot), sometimes the final consonant is doubled:

One-syllable words are always doubled.

rot → rotted
drag → dragged

For multi-syllable words, the final consonant is doubled if the last syllable is stressed.

regret → regretted
submit → submitted

Otherwise, the consonant is not doubled.

vomit → vomited
worship → worshiped

(British English does not follow this rule; consonants are always doubled.)

2. If the verb ends in -y preceded by a consonant, the -y changes to an -i before adding -ed

terrify → terrified
bury → buried

Otherwise, if the -y is preceded by a vowel, the -y remains and -ed is added.

destroy → destroyed
play → played

3. The above rules apply only to regular verbs. Other verbs, called irregular, are super annoying and have their own forms that you just have to memorize.
My LEAST favorites are Lie and Lay.

Lie → Lay (past tense) → Lain (past participle)
Lay → Laid (past tense) → Laid (past participle)

Here's a cheat sheet for Lie vs. Lay.