How do you say things in past tense ~ Japanese?

Question:

As the title says, how do you say things in past tense form in Japanese? For example, I >vacuumed<. I >cleaned< the bathtub. I >took< out the trash. >I dusted<. I >cleaned< my room. I >raked< the leaves.

Answer:

Well, in Japanese we can speak of formal and informal past tense.
Both adjectives and verbs have past tenses.
For verbs:
Well, formal past is easy, you should be familiar with the masu form (formal present), you just change masu to mashita and you have your past tense.
Informal past.
Well, informal past is far more of a drag, for this purpose they use the ta-form of a verb, which is conjugated the following wise from the dictionary form:
For ru dropping verbs:
You drop ru and add ta.
For u dropping verbs:
You exchange the last hiragana the following way:
mu, bu and nu will become nda.
su will become shita
tsu, u and ru will become tta
ku becomes ita
gu becomes ida
There are 3 exceptions:
suru -> shita
kuru -> kita
iku -> itta
For negative past:
Negative past is easier: For the formal negative past.
You add deshita to the formal negative form of the verb (masen)
For the informal negative past:
You treat the nai of the informal negative like a i-verb and put it to past form. (which means that nai will become nakatta)

For adjectives (You might know this or not be interested but whatever)
For na adjectives:
You add deshita (or datta to be less formal) for past.
For negative past: You add add deshita to ja arimasen (formal negative) (ja arimasen deshita)
Or once again put nai to past for informal negative past (ja nai -> ja nakatta)
For i adjectives:
You drop the final i and katta.
To make it formal you can add desu.
For negative past: You take the informal negatives ending: kunai and change it to past: kunakatta
Or you take the formal negatives ending: ku arimasen and change it to past: ku arimasen deshita.

Examples:
I went home.
Uchi ni kaetta (informal)
Uchi ni kaerimashita (formal)
I didn't go home.
Uchi ni kaeranakatta (informal)
Uchi ni kaerimasendeshita (formal)

The town was clean:
Machi wa kirei deshita (formal)
Machi wa kirei datta (informal)
The town wasn't clean:
Machi wa kirei ja arimasen deshita (formal)
Machi wa kirei ja nakatta (informal)
The town was high.
Machi wa takakatta desu. (formal)
Machi wa takakatta (informal)
The town wasn't high:
Machi wa takakunakatta (informal)
Machi wa takakuarimasendeshita (formal)