A quilt with mismatched seams will look like it was made by an amateur. A quilt with perfectly matched squares and seams will make the difference between handmade (crafted by an expert) and homemade (put together hastily by a novice). To line up quilt squares perfectly, there are a few things you can do, including pressing the fabric in the right way at the right times, making sure you have one-quarter-inch seam allowances and building the quilt into larger and larger square units.
Before cutting your fabric squares, press your fabric to get the wrinkles out. Use spray starch if necessary. Unless all of your quilt squares are precisely the same size, you will not be able to get your seams to match from the beginning.
Make a template out of cardboard or plastic: add one half inch to your desired square measurement for seam allowances. In other words, there will be one-quarter-inch extra around each square that will disappear behind when you sew your quilt squares together.
Sew squares together two-by-two with right sides together and raw edges even. You can use either a needle and thread or a machine for this step, but either way your seam allowances must be one quarter inch. In other words, your line of stitching must be one quarter inch away from the raw edges of the fabric square pair. If your quilt seam allowance deviates from this quarter-inch, you will not be able to match your seams without stretching your fabric out of shape.
Press quilt seams flat and then open out square pair. Place right-side-down on ironing board. Press the seams to one side. This step will help when lining up seams for the next step and to keep the right side of the quilt flat.
Sew your pressed square pairs together into small units of four, then eight, then 16 squares. Ideally, the quilt seam allowances meeting in the back will go in opposite directions. This will help prevent bumps from multiple layers of quilt fabric, but it will also help the seams nestle together and meet perfectly. Use pins to keep each seam meeting in place.
It is easier to match seams together when sewing squares together into larger and larger square or rectangular units. Squares sewn together in long strips are more difficult to work with and thus will be harder to keep matched.