Treat it just like you would a fabric strip you cut for the border.
Measure the quilt, cut that measurement from the roll and attach.
I would NOT soak it at any time. I don't know how scrappy the pieces were - bias edges, etc., but I'd probably sew it on to the quilt with the paper still attached to stabilize it.
Just use the same small stitch you used (I hope!) when piecing the paper. ;-) It will make it easier to take off.
When all four sides of the border are on, THEN I'd take the paper off. Great sitting in front of the TV mindless work. A bit messy, but mindless.
And then I'd stay stitch around the whole quilt - less than 1/4" from the edge where it will be covered by the binding.
Great idea for using up small pieces.
Please post a picture when you're done.