Native speakers mostly use this words as synonymous, but there are few exceptions. Firstly,"Красивий" is used only to describe physical attraction.But words"гарний/ прекрасний" sometimes can be used as "хороший(good)".For example, we can't say:"Це красива ідея , but "це гарна/прекрасна ідея" will be considered right .Here we actually mean "Це хороша ідея".We can also say "цей комп'ютер прекрасно працює" which is translated "This computer works good/great", not "This computer works beautifully " Secondly , "прекрасний" is translated as "very beautiful", so "прекрасний"is more beautiful than "гарний/красивий". For instance: Це прекрасна жінка - if you tell this everyone will think that the woman is incredibly beautiful, but sentence "це гарна/красива жінка" means that the lady has quite nice appearance

How do you use these words? For instance: Ukraine is a beautiful country. Україна - прекрасна країна. Yesterday I saw a beautiful woman. Вчора я бачив красиву жінку. That is a beautiful idea. Це гарна ідея. (To a girl) You are pretty. Ти гарна. (To a girl) You are beautiful. Ти прекрасна. (To a boy) You are handsome. Ти мужній.

Згоден з Venceslas Тільки: (To a boy) You are handsome. Ти вродливий. ( У "handsome" нема значення "мужній", хоча і йдеться саме про чоловічу вроду і привабливість).