In small piles - the 'real' stuff, the sort of daily wear collection, and everything else (and now wonder why I have an everything else pile if it isn't real and I don't wear it...). But I think if I'm honest, that's how I store all my things, not just earrings!
I went with a tray divided up into small boxes where I put the earrings in. I have actual drawers dedicated for my jewelry and it has space for laying out bracelets and inserts for rings, etc. to keep things separate and not get all tangled. (Yes, I have a lot!)
There are jewelry organizers that could fit, if not in the drawer, on top of the dresser or in a closet or something.
I was in the hardware store, and happened across the little organizer drawers that usually hold screws and such. They make a huge assortment of these, and mine is about 12" x 12", has a bunch of small drawers I use for the earrings, divided by color; and on the bottom six bigger drawers you can use for sets, necklaces or other bigger items. I only wear earrings, so I have the bottom drawers for spare items like powder makeup, etc. At one time when I had a lot of necklaces, and bracelets I had a wall rack that was really for belts or scarves. It was wooden with big wooden pegs that were perfect for separating necklaces or other big items, and keeping them from tangling.
I bought a hanging organizer that has about 18 clear zippered pockets on each side. I put it on a hook on the back of the door. I use it for earrings mostly, but you can fit bracelets and necklaces in a few of the larger pockets. Love it. I feel so organized when I look at it.