I don't yet have a picture of the finished shirt on me, but will add it when I get one.
I find all the seams with seam allowance. Usually, this is only the side seams.
I try on the shirt and use a safety pin to mark where I want to start widening the shirt. I take off the shirt.
I even out the measurements and make a chalk mark on both sides of the seam allowance. If the mark is on both sides, it doesn't matter which way I put the shirt into the sewing machine. Starting above the mark, I begin sewing on the original seam and taper my new seam into the straight part of the serged seam allowance, starting at the chalk mark. I continue sewing on this thread line until I reach the bottom of the seam. Repeat for the other seams.
Carefully, I use a seam ripper to remove the original seam stitches up to the point where I started the new seam. If the transition was smooth enough, there are no puckers. The one hazard for me is that if I am not exceedingly careful, I rip the fabric at least once. Depending on the size of the rip and quality of the shirt, I either fix this with a matching nail polish, a satin embroidery stitch, or some other sewing method.
Opening the seams like this doesn't give a great deal more room; I don't even know if the difference is visible. It does, however, make the shirt more comfortable to wear and I spend less time pulling at it. It also makes very clear the difference in the quality of my clothes. The black shirt in the picture retails at $90, which I didn't know when I bought it at a thrift store. It is better sewn (more stitches per inch, etc.) than a burgundy shirt I bought new for less than $20.