ようだ

ようだ is the written and formal-spoken form. みたいだ is its everyday spoken twin, casual where ようだ sounds stiff.

ようだ marks your own guess from evidence at hand. らしい instead points to outside information, and after nouns can mean "typical of" (春はるらしい).

ような／ように is the general "like/as" comparison, and takes any noun freely (子供こどものように). こんなふうに narrows to the manner, leaning on a demonstrative or quoted phrase (×りんごのふうに fails, りんごのように works).

降ふりそうだ reads how things look right now, and predicts what's about to happen. ようだ concludes a present state of affairs (どうやら雨あめのようだ).

ようだ covers a guess about anyone, even yourself (私わたしはどうも風邪かぜをひいたようだ). とみえる only guesses from outside evidence, never about yourself.

ようだ makes a real guess you believe (死しんだようだ, "he seems to have died"). かのようだ instead says a likeness you know isn't true (死しんだかのようだ).

ようだ ends a sentence as a guess about what's true (病気びょうきのようだ). のように describes what follows instead, and can't end a sentence (病気びょうきのように).

A verb ending in よう makes this the 〜おう／〜よう call (考かんがえようではないか). A noun＋の, な-adjective＋な or plain form makes it ようだ (まるで病気びょうきのようではないか).

ようだ's よう states your own guess, and ends the sentence (雨あめが降ふるようだ). ようでは freezes the same よう into an if-form, it can't end a sentence alone.

ようだ guesses what something looks or seems like (誰だれもいないようだ). ようがない instead says no method is left to do something (直なおしようがない).

ような気きがする reports your own felt hunch, with 気きがする as the real verb. ようだ alone instead reports a guess from outside evidence.