Take the two ends of the binding strip and sew them together with a 1/4" seam allowance. Make sure that the strip isn't twisted.
Now, you should have a continuous loop of binding. Press the seam open.
Attach the binding to the quilted piece as you would normally, mitering the corners as usual.
And here it is, all attached! Isn't that slick?
Press the binding away from the front of the quilt. (it's not easy on a tiny piece!)
Here it is, all finished!
If you have any questions, I'll try to answer them in the comments.
Go forth and bind ALL the tiny things!