Once you have all of your blocks made, and you are finished deciding how they'll be laid out, it's time to sew them all together. Start with two blocks, sew them together with a 1/4 inch seam, and then carefully pick out the newspaper at the start and end of each seam. You only need to pick out about one square inch from each corner (front and back!) but if you don't, the paper will be trapped inside the seam allowance of the next joining step. I should have taken a picture of what I mean...sorry!
Once you have all the pairs sewn together, start sewing those to each other, being careful to keep them in the right order. And pick out the paper in the corners of every seam as you go. Also, pressing the seams open at every step will keep things nice and neat. Pretty soon, your quilt top will be assembled and it will look something like this:
I draped the whole thing over my ironing board and set to work picking our the paper while I watched tv. I think it was done in about 2 hours. Again, if you don't want to mess with this step, use a lightweight muslin fabric for your foundation. And if you are working with newsprint like I am, be careful not to touch the front of the quilt top while you are picking out the paper. It gets a little messy.