1Fast, quick, rapid, swift — used to describe high speed of motion or action, where something covers a lot of ground in little time. In this speed sense, the word is conventionally written 速い; writing 早い here is generally felt as the wrong kanji choice.
新幹線は速いから、東京から大阪まで二時間半で着く。
The Shinkansen is so fast that you can get from Tokyo to Osaka in about two and a half hours.
兄は足が速くて、運動会ではいつも一位だった。
My older brother is a fast runner — he always came first at school sports day.
最近のパソコンは処理が速くて、動画編集も快適にできる。
Recent computers are so fast that even video editing runs smoothly.
あのピッチャーの球は150キロを超えるほど速い。
That pitcher throws so fast that his pitches go over 150 km/h.
2Early — at a point in time before a reference point or before what is typical (early morning, an early hour, earlier than scheduled). In this sense the word is written 早い.
朝早い時間に散歩すると、空気が気持ちいい。
Taking a walk early in the morning, the air feels wonderful.
約束の時間より三十分も早く着いてしまった。
I ended up arriving a full thirty minutes earlier than the agreed time.
春が近いせいか、今年は桜が咲くのが早い。
Perhaps because spring is just around the corner, the cherry blossoms are blooming early this year.
3Premature, too soon — describes something happening before the appropriate moment. Often used to push back on hasty conclusions or decisions: 「結論を出すには早い」 (it's too soon to draw a conclusion). Written 早い.
その件について結論を出すのは、まだ早すぎる。
It's still too early to draw a conclusion on that matter.
諦めるのはまだ早いよ。最後までやってみよう。
It's too soon to give up — let's see it through to the end.
4Quick or easy in the sense that a particular method gets you to the result with the least time and effort. Used in patterns like 「〜したほうが早い」 (it's quicker to do X), expressing efficiency rather than raw speed. Written 早い.
この時間は道が混むから、地下鉄で行ったほうが早い。
The roads are jammed at this hour, so it'll be quicker to take the subway.
説明書を読むより、彼に直接聞いたほうが早いよ。
Rather than reading the manual, it'll be quicker to just ask him directly.
5Used in the somewhat literary patterns 「〜するが早いか」 / 「〜するより早く」 to mean 「no sooner had X happened than Y」 — Y starts the very instant X occurs. Close in meaning to 「〜したとたんに」 / 「〜するや否や」.
ベルが鳴るが早いか、生徒たちは一斉に教室を飛び出した。
The moment the bell rang, the students all rushed out of the classroom at once.
母は私の顔を見るより早く、何があったのか察した。
Even before she saw my face, my mother had already sensed that something had happened.