How do we wish someone to get better? When we know somebody is sick, how can we wish them to get better? What are the best ways and also the standard ones to do that?

I'd like you to differentiate among some things, if and when applicable:


Tell someone directly (get better soon) VS tell someone's relative/friend (I wish your __ gets better soon);
When the cause is something "light" (like a flu) VS something more serious (being in the hospital);
When there is confidence with the interlocutor VS when there's no confidence;
etc... Other things that I might have forgotten.
One common phrase is this one, where X is the somebody in your question:


  祝X早日康復/祝X早日康复。
  Zhù X zǎo rì kāng fù


For example, 祝你早日康復/祝你早日康复, which can be translated into "wish/hope you'll recover soon." or "wish/hope you'll make a speedy recovery."

Vocabulary:


  
  祝 (zhù) = Wish
  你 (nǐ) = You
  早日 (zǎo rì) = in the near future, soon
  康復/康复 (kāng fù) = recover from illness
  


This phrase can be used in most situations (mostly formal, informal and situations 1, 2 &amp; 3 in your questions).

For "light" sickness, say a cold or a headache, people often say:


  
  多休息/多休息 = Take more rest.
  Duō xiū xí
  多保重/多保重 = Please take care.
  Duō bǎo zhòng
  小心別又著涼了/小心别又着凉了 = Please don't get cold again.
  Xiǎo xīn bié yòu zháo liáng le
  


You'd often hear parents or elderly relatives say Example 3 to their kids or young people in the family when they have a cold.