Growing Mushrooms?

I'm attempting to grow mushrooms. No, not the psychedelic kind, the normal edible, button mushroom kind. Why you ask? For the past two summers I had a vegetable garden at my parents house, and seeing as I'm not longer there enough to upkeep a garden, and I can't really grow vegetables (I only really enjoy growing things I can eat, like vegetables or berries or sunflowers, ect) in our apartment. Lilly does however really enjoy mushrooms, and we tend to eat a fair amount of them. Mushrooms are something, in theory, that we could successfully grow in our apartment, so I figured why not? 

I'm attempting to grow them in this plastic storage container. In it is some dirt, under some compost (which consists of a lot of ash), under some coffee grounds. Below is the mushroom spawn I got online (I got it from eBay, for about $8 including shipping). 

After spreading the spawn over the top, I put wet paper towels over it. Fingers crossed this works, cause it'd be sweet to have our own personal supply of mushrooms over the summer. And if it does work I'll be sure to update with a post all about it. Until then, I'll see you next Tuesday!