First and foremost, be accurate during the piecing process. Keep the 1/4 inch seams consistent. Inaccurate piecing will cause the quilt top to be off-square and often result in poor results during the quilting process. Each inaccurate seam compounds across the quilt.
It is also a good habit to press the seams as you construct the top and trim any excess threads.
Trim the backing so that it is square with respect to the length and width of grain. The backing is the first to be mounted on the frame and the top edge is assumed to be squared. If it is not, then the backing will end up at an angle. The best scenario is that backing is one piece. There is now a good selection of material up to 108" wide. If the backing is to be pieced, the preferred method is to join across the width. As mentioned earlier, I require 5 inches on each side larger than the top and another 10 inches to the length to allow for proper mounting. Another check to do is to turn the quilt top over. If the top has both light and dark threads, be sure to clip any dark threads that may be falling onto light sections. They will definately show through and once quilted, impossible to remove.
Mr Burton has also written up a tutorial on how to properly measure and cut borders. It eliminates bulk created when quilting, especially at the right side and bottom. If you would like a copy, let me know and I will email the document to you. It is in PDF format.
Special note: If you are planning on using a polyester plush backing, such as fireside or minky, I will need to apply a temporary spray of 505 to the backing to adhere to the batting. This is done each time the quilt is forwarded. These fabrics have a lot of stretch and are slippery and are notorious for curling along the edges. This would be considered an extra cost in materials.
If you plan to make a top that is composed of stretchy knit material, as in making a t-shirt quilt, you must ensure to apply an iron-on stabilizer before piecing. Without it, the knits would stretch and look terrible.