In short

All three mean roughly “it seems”, and the difference is whose evidence you are standing on. ようだ (yō da) is your own - you looked, you reasoned, you commit to it. みたいだ (mitai da) is the same claim in casual clothes. らしい (rashii) says the evidence came from outside you - people say so, that is the word going round - which quietly moves the responsibility off your shoulders. On top of that, ようだ and みたいだ do a second job English needs a different word for: resemblance, 氷のように冷たい (kōri no yō ni tsumetai, cold as ice).

The rule

Step 1 - Attach to the plain form, but watch nouns and な-adjectives.

All three sit on the plain form from lesson 17, so the verb in front of them is plain even when the sentence ends politely: ×降りますようです -> 降るようです. Verbs and い-adjectives therefore behave identically for all three. Nouns and な-adjectives are where they split:

• ようだ takes の and な, because よう is really the formal noun 様 (“appearance, manner”). You are literally modifying a noun, so you link to it the way you link to any noun: 雨のようだ ame no yō da, 静かなようだ shizuka na yō da.
• みたいだ and らしい take the noun bare - no の, no な, no だ: 雨みたいだ ame mitai da, 静かみたいだ shizuka mitai da, 雨らしい ame rashii, 静からしい shizuka rashii.

If you remember only one thing from this lesson, remember that よう behaves like a noun and the other two do not.

Step 2 - ようだ: my eyes, my nose, my reasoning.

ようだ presents a conclusion you reached from evidence you have. You see the open window, you smell the smoke, you notice the lights are off - and you announce the inference: 誰かいるようです (Dareka iru yō desu, it seems someone is here). Because you own the reasoning, ようだ commits you to it. It also leans formal and written: reports, articles and careful speech use ようです where a friend would say みたいです.

Step 3 - みたいだ: the same thing, spoken.

みたいだ is the colloquial equivalent of ようだ. Same evidence, same commitment, plainer register - and it is by far the more common of the two in everyday conversation. Keep it out of essays, business e-mail and anything written to be read by strangers, where ようだ is expected.

Step 4 - らしい: the evidence is not mine.

らしい marks the ground of the claim as outside the speaker - hearsay, reputation, a rumour, something you overheard, general word-on-the-street. You are still inferring (that is what separates it from plain reporting), but from other people’s information, so らしい puts distance between you and the claim: 山田さんは引っ越すらしいです (Yamada-san wa hikkosu rashii desu, apparently Yamada is moving) - and if it turns out to be false, you were only passing on what is being said.

Step 5 - らしい versus 伝聞のそうだ. Both point away from you, but they are not the same move. そうだ (lesson 42) relays a specific report more or less verbatim - and it often names that source (天気予報によると…降るそうです). らしい draws a conclusion from information floating around, without naming anyone. So そうだ makes you a messenger; らしい makes you a cautious analyst.

Step 6 - The other らしい: “a proper X, typical of X”.

Attached to a bare noun, らしい can instead mean “having the qualities you expect of that noun”: 男らしい otoko-rashii (manly), 学生らしい服装 gakusei-rashii fukusō (clothes befitting a student), 今日は春らしいですね Kyō wa haru-rashii desu ne (today feels properly like spring). Its negative 〜らしくない is extremely common and means “unlike him/her/it, out of character”: 彼らしくないですね (Kare-rashikunai desu ne, that’s not like him). Context separates the two らしい: after a full clause it is inference, after a bare noun describing that noun’s own character it is “typical of”.

Step 7 - Resemblance and simile: よう / みたい, not らしい.

This job belongs to ようだ and みたいだ only. Noun + の + ような + Noun (“a N like a N”) and Noun + の + ように + Verb/Adjective (“like a N”, adverbially): 氷のように冷たい kōri no yō ni tsumetai, 天使のような人 tenshi no yō na hito (a person like an angel). The adverb まるで marude (“just, exactly”) is the standard partner for a full simile: まるで夢のようです (Marude yume no yō desu, it’s just like a dream). Casual speech swaps in みたい: 氷みたいに冷たい, 子どもみたいな人.

Step 8 - Adverbial ように for manner and instruction.

ように also means “in the manner of, as”, pointing at a model to copy: このように kono yō ni (like this), 図のように zu no yō ni (as in the diagram), 私が言ったように watashi ga itta yō ni (as I said). This is the form you meet in manuals and demonstrations: このようにしてください (Kono yō ni shite kudasai, please do it like this). It also builds 〜ように見える／聞こえる (yō ni mieru / kikoeru, looks as if / sounds as if).

What this lesson is not. The purpose ように (“so that…”) is a different construction and lives in lesson 43. Evidence-free guessing (でしょう, かもしれない) is lesson 32, and the stronger はずだ／に違いない is lesson 53.

Forms & patterns

Attachment - the whole difference is in the last two rows of each block:

Inflection - ようだ and みたいだ bend like な-adjectives, らしい like an い-adjective:

For the inference らしい, the past and the negative normally go inside, on the plain form (降ったらしいです, 降らないらしいです); らしくない almost always belongs to the “typical of” らしい, and inference らしかった is mostly found in past-tense narration (“it seemed that …”).

Whose evidence? らしい against its two neighbours:

Choosing among all six:

Examples

Common mistakes

• 雨が降りますようです。 (Ame ga furimasu yō desu.) -> 雨が降るようです。 (Ame ga furu yō desu.) - ようだ sits on the plain form; the politeness is carried once, at the end.
• 今日は雨ようです。 (Kyō wa ame yō desu.) -> 今日は雨のようです。 (Kyō wa ame no yō desu.) - よう is a noun, so another noun links to it with の, exactly as in 雨の日.
• この部屋は静かようです。 (Kono heya wa shizuka yō desu.) -> この部屋は静かなようです。 (Kono heya wa shizuka na yō desu.) - and for the same reason a な-adjective keeps its な before よう.
• 雨のみたいです。 (Ame no mitai desu.) -> 雨みたいです。 (Ame mitai desu.) - みたい is not a noun, so nothing links to it: nouns and な-adjectives attach bare (静かみたいです, not ×静かなみたいです).
• 彼は男らしいでした。 (Kare wa otoko-rashii deshita.) -> 彼は男らしかったです。 (Kare wa otoko-rashikatta desu.) - らしい is an い-adjective: past らしかった, negative らしくない. There is no ×らしいでした.

Tips

• よう is a noun in disguise. 様 means “appearance, manner”, which explains everything odd about it in one stroke: 雨のよう, 静かなよう, ような人, ように冷たい. Say to yourself “attach to よう the way you would attach to any noun” and you will never write ×雨ようだ again.
• みたい and 見たい sound identical. 映画が見たいです (eiga ga mitai desu) is I want to see a film; 映画みたいです (eiga mitai desu) is it’s like a movie. The tell is the structure, not the sound: 見たい is the verb 見る’s ます-stem 見 plus たい (lesson 14), so it states a wish and its object takes が (or を), while みたい attaches straight onto a bare noun or a full plain form.
• らしい is the polite way to gossip. Because it grounds the claim outside you, らしい lets you pass on news without vouching for it. That is also why it is a bad choice for something you saw with your own eyes - saying 雨が降ったらしいです while standing in the rain sounds absurd; there you want ようです or みたいです.
• Written or spoken decides ようだ vs みたいだ. They differ in register, not meaning. In a report, an exam answer or an e-mail to a stranger, write ようです; with friends, say みたいです. When in doubt in a formal setting, ようです is never wrong.