To conjugate a う-Verb into its past tense, you must first alter its final kana, similar to other う-Verb conjugations. After this, you will attach the auxiliary verb た for the casual form, or ました for the polite form. The way the final kana changes for the casual past tense has several variations, so let's examine them.

• クッキーを作(つく)った。クッキーを作(つく)りました。
  I made cookies. (Example of a verb ending in る)
• そのジョークで笑(わら)った。そのジョークで笑(わら)いました。
  I laughed at that joke. (Example of a verb ending in う)
• ついに試合(しあい)に勝(か)った。ついに試合(しあい)に勝(か)ちました。
  I finally won the match. (Example of a verb ending in つ)
• 先生(せんせい)に質問(しつもん)を聞(き)いた。先生(せんせい)に質問(しつもん)を聞(き)きました。
  I asked the teacher a question. (Example of a verb ending in く)
• 彼(かれ)は駅(えき)まで急(いそ)いだ。彼(かれ)は駅(えき)まで急(いそ)ぎました。
  He hurried to the station. (Example of a verb ending in ぐ)
• ゲームのキャラクターが死(し)んだ。ゲームのキャラクターが死(し)にました。
  The game character died. (Example of a verb ending in ぬ)
• 公園(こうえん)で友達(ともだち)と遊(あそ)んだ。公園(こうえん)で友達(ともだち)と遊(あそ)びました。
  I played with my friends at the park. (Example of a verb ending in ぶ)
• 昨日(きのう)、この本(ほん)を読(よ)んだ。昨日(きのう)、この本(ほん)を読(よ)みました。
  I read this book yesterday. (Example of a verb ending in む)
• 彼(かれ)と電話(でんわ)で話(はな)した。彼(かれ)と電話(でんわ)で話(はな)しました。
  I spoke with him on the phone. (Example of a verb ending in す)

As shown in the examples above, the endings become った, いた, いだ, んだ, or した. These are identical to the endings for the て form, just with た instead of て. In cases where the ending becomes voiced (e.g., いだ), this is a natural sound change that makes the word easier to pronounce. It is not related to the auxiliary verb だ.

The polite past form for う-Verbs is much more regular. You simply change the final kana from its う-row vowel to its い-row vowel (such as う to い, or く to き), and then add ました.

• 駅(えき)の前(まえ)で友達(ともだち)に会(あ)いました。
  I met my friend in front of the station.
• 昨日(きのう)、遅(おそ)くまで働(はたら)きました。
  I worked until late yesterday.

The auxiliary た attached to a verb can carry one of three main nuances.

Past: 過去(かこ) - Refers to an action that occurred at a specific time before now. (Did/Was)

Completion: 完了(かんりょう) - Marks the conclusion of an action, often one that just finished. (Done)

Continuation: 存続(そんぞく) - Indicates a state that resulted from a prior action and still persists. (Has been done)

• 去年(きょねん)、日本(にほん)へ行(い)った。
  I went to Japan last year. (An example of past)
• あ、お父(とう)さんが帰(かえ)った。
  Oh, Dad just got home. (An example of completion)
• テーブルに置(お)いてあったコップが割(わ)れた。
  The cup that was on the table broke, and is now in pieces. (An example of continuation)