Advance apologies: my camera didn't like taking really focused pictures of denim, so many of the denim pictures are slightly fuzzy.
1. For a normal flat-felled seam, start by sewing your fabric WRONG sides together with a 5/8" seam allowance. Backstitch at both ends. You can barely see my thread below--it's pink. An inside-out flat-felled seam is exactly the same, except you start the normal way with your fabric right sides together.
2. Trim the seam allowance of the back piece if this is a vertical seam or the bottom piece if it is a horizontal seam down to 1/4". You can eyeball this measurement as just more than half of the seam allowance width.
Inside-out version: fabric right sides together, back seam allowance trimmed to 1/4".
3. For both versions, press the seam allowances toward the back, over the trimmed seam.
4. Use your fingers to tuck the longer, top seam allowance around and under the shorter one.
Add pins to hold everything in place as you sew it.
For the inside-out version, it is actually slightly better if you put your pins on the right side of the fabric. I failed to do that on mine, and it turned out okay. You want the outside of the seam to look best, so it's a good idea to pin and sew from that side if you can.
5. Sew 1/4" away from the first line of stitching, folding down the fold of the seam allowance. This should be just shy of 1/8" inside the folded edge. Hard to really tell in the photo where my folded edge is, sorry.
The finished view! Two rows of stitching on the outside of the garment: a very strong, durable seam.
For the inside-out version, try to sew from the right side of the fabric if you can. If you aren't comfortable doing that (you might sew off of the edge and not catch the fold) it is okay to sew from the back side. This is what it looks like finished on the inside:
Here's what it looks like on the outside. You can see the original seam and one line of stitching holding everything in place.
It may seam like this method takes a long time, but it actually can go quite quickly, especially on short seams. Taking time to finish a seam properly will increase the quality and life of whatever it is sewn into.