Used adverbially to mean well, properly, or suitably (doing something in an appropriate or satisfactory way).
この書類は機密ですから、よろしく取り扱ってください。
These documents are confidential, so please handle them properly.
機械の操作は説明書を読み、よろしく行ってください。
Read the manual and operate the machine correctly.
スタッフには安全に気をつけて、よろしく作業するように伝えた。
I told the staff to work carefully and properly.
A set phrase used in greetings or requests meaning 'please treat me well,' 'best regards,' or 'please take care of (someone/thing)'.
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. I'm Tanaka. Please take care of me.
来月からチームに入ります。皆さん、よろしくお願いします。
I'll be joining the team from next month. Everyone, please take care of me.
部長によろしくお伝えください。
Please give my regards to the manager.
お願い事があるときは、『よろしくお願いします』と言うのが丁寧だ。
When asking a favor, it's polite to say 'yoroshiku onegaishimasu.'
Used in the pattern '...よろしく' to mean 'as if ...' or 'in the manner of ...' (used metaphorically to describe behaviour or appearance).
彼は王様よろしく振る舞い、周りの人を困らせた。
He behaved as if he were a king, upsetting the people around him.
先生よろしく生徒たちに注意を促した。
He admonished the students in a teacher-like manner.
彼女は母親よろしく子どもたちの世話をした。
She took care of the children as if she were their mother.
An older/literary usage meaning 'by all means' or 'of course.' This is somewhat archaic and not common in everyday speech.
この仕事は君にしかできぬ。よろしく頼むべし（文語的）。
This work can only be done by you. You must be relied upon (literary/archaic).