Where are the key fragments?

Only with wins. Each key you find in the ~30 day cycle makes it harder to find the next. Resets once every ~30 depending on when you first received hextech loot.

Here's some nice info on key fragment drop rates (i'm not sure the formula is current):

https://www.lolriotpls.com/2016/04/leagueoflegends/hextech-crafting-key-fragment-droprate-formula/

Also, you won't earn key fragments (or chests) if you are under a chat restriction or are in a reform period following a punsihment.