〜た

The た-form is the plain past affirmative — "did X." 食べた = "[I] ate." Polite past is 食べました; informal past is 食べた. The conjugation pattern is identical to the て-form (same consonant-class table), just with た instead of て: 書く → 書いた, 待つ → 待った, 飲む → 飲んだ.

た marks completion or pastness in declarative sentences. But it also has two non-past uses worth knowing:
• Recall / sudden memory: あ、わかった! — "Oh, I get it!" (the moment of getting it, not the past).
• Polite request via question: ちょっと待った? — colloquial "could you wait a moment?" (rare; mostly in fixed expressions).

In relative clauses, the past form often translates as English present-perfect or simple past depending on context: 昨日見た映画 — "the movie I saw yesterday."

Negative past is 〜なかった (plain) or 〜ませんでした (polite). I-adjectives form past with かった (寒かった); na-adjectives and nouns add でした / だった to the unconjugated form.