What is the difference between изменить and менять?
When would you use each of these verbs?

Question

Answer

Менять (imperfective) - поменять (perfective) to substitute one with another.
Она часто меняет занавески. (использует другие занавески)

изменять (imperfective) - изменить (perfective) to change the initial subject, to make it better/worse/different without having another one.
Мы изменили оформление - we changed the way it looks.
Невозможно изменить человека. - it's impossible to modify a person.
Also: изменять + dative = to cheat on smb. Она изменяет ему (с коллегой). - She's cheating him (with her colleague).

Sometimes they are interchangeable: 
Нужно поменять пароль.
Нужно изменить пароль.

Answer

"Изменить" -- to change smth. or someone, for example, to change the nature of a man, or to change adverse circumstances. "Менять" -- as a rule, to change smth. to smth. Money to goods, favours to benefits, etc.

Answer

менять - to change(when it's in progress). 
изменить/поменять - to change(when you are talking about something what should be changed or have already been changed).

Examples: 
the weather has changed - погода изменилась
the weather is changing - погода меняется
you should change your behavior - ты должен изменить/поменять свое поведение
etc...

Answer

"менять" has two basic meanings:

1) 'to change, to make different'. Eg: менять окружающую среду, менять образ жизни, менять  прическу etc. In this meaning, "изменить" is the perfective pair to the imperfective "менять" (along with another imperfective form "изменять").

2) 'to exchange for / to replace with another' (usually meaning physical exchange/replacement). Eg: менять вещи местами, менять одежду/обувь -- to change dress/shoes etc. In this case, "изменить" cannot be used as the perfective pair to менять.