Jan, here are a few photos of how I do it. I have deliberately used contrasting thread so that you can see it more clearly. You have to cut your fabric on the bias at 3/8". Then you use a running stitch to attach it. Cutting it on the bias means that you can manipulate it any way you want to. The fabric you use would also have a bearing on this. I usually use batiks for needle turn as it is easier to manipulate without getting any stray threads.
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Next you finger press the fabric over the stitched line. And then using your needle and thumb you fold the fabric under towards the inside and stitch down with small stitches. Try to catch the underside of the bias strip when you come back up through the background fabric and then your stitches will barely show.
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When you have finished you can press it with an iron, but this is what it looks like without pressing. It measures 1/8".
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You could make the strips narrower by using 1/4" bias strips. Hope that helps. And have a good day at the show.