In what contexts should I use за or для when saying "for" or "to" something or someone?
For example, I understand that it is proper to use "за" when calling out a toast: "за Россию!". But that you should use "для" when saying for example: "для меня это важно".
Are there any rules concerning the usage of these words?
За:
support or backing: сражаться за Родину, голосовать за законопроект
anything involving trade or exchange, as well reward, punishment, gratitude or apology: продать за сто рублей, поблагодарить за приём, ответить за свои преступления;
acting on another's behalf, instead of them: сделать за сына домашнее задание;
Для:
doing something for someone else's benefit, but not instead of them: найти для сына невесту;
general intended or affirmed purpose of a thing: вилка для сыра, книга для детей, место для меня;
subjective measure of a quality: здесь для нас слишком жарко;
"too X/(not) X enough for a Y", "pretty X as Ys go" constructions: неплохо для начинающего.
Note also that for in English and за in Russian can both have meanings referring to time, but those meanings are different in each case and do not translate into each other. For two weeks is, depending on context, две недели (plain accusative) or на две недели, whereas за две недели is, again depending on context, in two weeks or two weeks before (if followed by до).
За is more like pro- prefix in English. It signifies that you're not going to do anything material for the object, other than feeling good for it. When drinking for something, supporting your sports team, you use за.
You use для when it ought to be followed by actions in support of the object.
(One exception is, perhaps, voting: Голосовать за Пупкина means casting vote for Pupkin. But given the state of Russian democracy maybe it isn't an exception at all)
This is mocked in Понедельник начинается в субботу, where they make a wall newspaper called За передовую магию, this task handled to the most inept persons in the collective.
