EVERYTHING- Implies all there is, used in affirmative sentences. eg. Everything went wrong today. (It means, from the beginning to the end nothing was ok.)
ANYTHING-Implies whatever -good, bad, real, fantastic. Used in interrogative and negative sentences, always accompanied by an auxiliary to mean almost nothing. Alone, in affirmative sentences it gives way to a fantastic array of possibilities.
What would you like to have for lunch? Anything will be fine, I don't crave nothing in particular. (It means the person that is going to eat is not really hungry or doesn't care what the food will be. Anything means whatever you give me will be fine.)
I didn't see anything when I came in. (It means there was nothing.)
DON'T CONFUSE ANYTHING WITH NOTHING
NOTHING-Implies total absence. Used in sentences with affirmative verbs to express a negative idea. There was nothing in the room that seemed interesting. (The room didn't have what was thought interesting.)
There was nothing in the room. (The room was empty.)