1An adverb meaning 'properly', 'appropriately', or 'as is fitting'. The continuative form of the adjective よろしい, mostly seen in formal writing and set phrases like よろしく取り計らう or よろしくご検討ください. Rare in casual speech in isolation. Usually written in kana.
この件は現場の判断でよろしく取り計らってください。
Please handle this matter appropriately at the discretion of the people on site.
ご多忙のところ恐縮ですが、よろしくご検討くださいませ。
I'm sorry to trouble you when you're busy, but please give this your due consideration.
事情をよろしくわきまえて対応してくれた。
He dealt with it showing a proper understanding of the situation.
2A set greeting/request phrase. In the form よろしくお願いします, used widely in self-introductions, requests, and farewells to ask for the listener's goodwill, cooperation, or assistance. In the form 〜によろしく, it means 'please give my regards to ~'. One of the first essential phrases a Japanese learner encounters. Usually written in kana.
はじめまして、田中と申します。どうぞよろしくお願いします。
Nice to meet you. My name is Tanaka. Pleased to make your acquaintance.
来週からこのチームに加わります。よろしくお願いします。
I'll be joining this team starting next week. I look forward to working with everyone.
お母さんによろしくお伝えください。
Please give my regards to your mother.
じゃあ、後はよろしく！
Alright, I'll leave the rest to you!
今年もよろしくお願いいたします。
I look forward to working with you again this year.
3Used in the pattern 〜よろしく to mean 'just like ~', 'in the manner of ~', or 'as though one were ~'. Compares behaviour or appearance to whatever precedes it, in a somewhat literary or written register.
彼は王様よろしく上座にどっかりと腰を下ろした。
He plopped himself down at the head of the table just like a king.
課長は探偵よろしく事件の細部まで質問してきた。
The section chief grilled us about every detail of the incident, just like a detective.
子どもたちは小さな大人よろしく落ち着いて席に着いた。
The children took their seats calmly, like tiny adults.
4An archaic/literary usage in the pattern よろしく〜べし, meaning 'by all means' or 'one ought to ~'. Almost unused in modern speech; mainly found in classical-style writing or kanbun-influenced prose.
学ぶ者はよろしく古典をひもとくべし。
Those who learn ought, by all means, to consult the classics.