If you look at the Gift Laptop Quilt, the quilting is the part where you are putting the stitches in around the flower design. Many times the hardest part is the piecing of a quilt top-which is what you are talking about doing. In this case the batting is sandwiched between the backing and the quilt top. You decide how big you want the quilt and when you have put all your scrap material together make the quilt top an even edge all the way around... Be sure if the top edge is 44" that the bottom edge of the quilt top is 44" and if the side is 72" that the other side is exactly 72".
Your backing if you are going to pull it around so you don't have to make a binding separate will need to be that much bigger... so it would need to have an extra 4.5" all the way around to be able to fold it over 2 and under 1/2" to have a smooth fold under edge on the 2" quilt binding of 1/2". Your batting will be 2" wider than the quilt top and the quilt binding edge will just come over your quilt top so it doesn't infringe on any design.
I will give you pictures in the article so you can understand. You pin your 3 pieces together like a sandwich and baste round the edge or spray baste with a commercial quilting spray glue. Check the reviews of different basting glues on the internet so you can eliminate the brand that has the worst reviews. I just pin in the center and machine baste large stitch around the whole piece.You can stitch in the ditch of the seams of your pieces on your quilt top or just turn over your quilt after you have sandwiched it together and give yourself a patter you want to quilt it. You use a freemotion quilting stitch on your machine so you can mover your quilt around as you sew the sandwich together, or you can handquilte as Great Grandma's and those without sewing machines have always done.
You can also handtie the quilt. If you have a good compressed cotton batting, you can tie as far as 10" apart. That is use a yarn or many strand embroidery floss to tie the quilt.... You tie just like any square knot and the ends are usually about 2" so you would have a yarn or embroidery floss of 4.5" so you have plenty to tie an x square and leave the tails straight up on the top for decoration besides functionality. I will do a couple of small wall hanging examples.
I will do an Article explaining what quilting is and the easiest ways to do piecing and the quilting.