Here we're using a cushion stretcher (seam stretcher), or cushion equalizer. It's adjustable and locks in place making our job much easier. You can also use upholsterers pins, or that expensive tool, the clothes pin. I'm using a 3 1/2" curved needle and nylon hand sewing twine for this job. I'll use black thread so you can see me working and also so you can see that when this done right, the thread doesn't show anyway (maybe they should teach this in medical school). For light weight fabrics use a thinner, smaller needle and thinner but strong sewing machine thread. Also, it's a good idea to have marked the center of the plates to help you keep them aligned.
Tie a knot in the end of the twine and thread needle. Start by going inside the pillow to the right so as to lap the sewing machine stitch. See above photo.
Next take about a 1/2" bite through the welt fabric, less for lighter weight fabric. Avoid going into the cord itself. Pull tight.
Hold your thread straight up and down to determine where your needle should enter the upper plate. Continue this method until you've lapped the spot you sewed on your machine. If it looks as if the top plate, for example, is going to have more fabric than the bottom, then insert your needle a little to the left of normal on the top plate. This will help take up some of the slack.
When you're finished sewing wrap the twine around the needle a time or two and insert it into the pillow fabric or welt. Hold the thread snugly, close to the spot where the needle goes in. This will produce a knot which can stay inside the fabric keeping your work from coming loose. You'll usually hear a little popping sound when you successfully tug the knot into the right place. Cut off the excess twine. Now that you've learned how to hand sew you're really on your way to be an upholsterer!