First align your pattern pieces with wrong sides together, and the right side out. This is the opposite of what we are used to doing when making a regular seam. Assuming you are using the standard 5/8ths inch seam allowance, sew the first seam using a 2/8ths (or 1/4 inch) seam allowance.
At this point, your seam is visible on the outside of the garment. Next, trim to within 1/8th of an inch of the seam line.
Now turn your piece wrong side out, and press.
A second seam is now sewn, using a 3/8ths of an inch seam allowance. The 2/8ths we used earlier, plus the 3/8ths taken now, add up to the traditional 5/8ths inch seam allowance. Of course, all of these measurements can be changed if you are dealing with a different seam allowance. French seams with tiny seam allowances are often used when sewing sheer fabrics as they prevent raveling and neaten the seam without adding bindings that can also add bulk.
Once this step is completed, so is your French seam! French seams are useful, as described above with sheer fabrics, but also whenever you want to cover over the seam edges and don't want to use other seam finishes. I've used them extensively when sewing long heavy skirts in period clothing like Medieval gowns and the like.
Thanks very much for sewing along! If there are other techniques you'd like to see demonstrated, please feel free to comment and let me know!