A little help...what do you do with a CSGO weapon case?

I'm definitely not the best person to answer, but at least I know how the system works.

Basically, there're different types of cases, containing skins / knives of various rarities, and the keys used to open them.
Cases are randomly dropped during matches, while keys must be purchased (they usually cost around $2.5) or traded.

Some risk-loving players might want to gamble with keys, opening cases, and hoping to find some expensive items inside them.
Others would just sell the cases on the community market, to make some quick Steam wallet cash.

TL;DR: if you think you will start playing, and invest a lot of hours into the game, you might consider opening that case (mind that those items are purely aesthetic, and don't offer ingame advantages).
Otherwise, just sell it for a small profit (or trade it for cards).

EDIT: Too slow (>_<)