I decided it needed bright colors and polka dots too. The first step was to pop the lid off by unscrewing it. Then I just laid it upside down on top of my fabric and stapled the front edge.
You're going to need a helper for the next part to get your corners nice and tight. I would suggest picking one that has opposable thumbs and not my furball.
With help, fold the corners of your fabric in like a present and staple in place.
Pop the lid back on, screw in place, and inspect it to make sure it's on tight and won't slide when a child sits on it. I had more help with this stage, as you can see.
I love it! You could easily do this with other piece of furniture too.
While I was at it, I updated a few of our crate seats too (using the same process). You can see that original tutorial here.