To find a Key, you need to break Tiles that are hiding it. In order to break a Tile, you need to create a match on the same space. The Key location is random. You need to uncover the whole Key before you can claim it for the Quest completion.
Note that Tiles can have up to 3 stages and will not disappear until all the stages are cleared. The last stage is cracked enough to reveal the position of the Key but you still need to break it completely to free the Key.