There are loads of fantastic tutorials available online for different methods of doing a bound edge with knit fabrics. I think over time I've tried nearly all of them and I use two or three different methods depending on the situation. In my mind the methods generally can fit into one of two categories either worked flat or worked in the round. I LOVE doing my binding flat (i.e with one shoulder seam of a neckline still open), because this opens up the possibilities of using a wider variety of fabrics for the binding. If you bind flat then you can simply cut the binding longer than required and then stretch as you stitch it on, later cutting the binding to length. This means the amount of stretch a fabric has isn't as important (you can even cut your binding on the bias if need be), and you don't have to do some fancy guesswork or complicated maths to work out the binding length. If you bind in the round you need to know the exact length of the binding before starting as the first step is to join the binding into a circle, and this length will vary hugely depending on the stretch and recovery of the knit used.
BUT when working flat the final step after completing the binding is to stitch the second shoulder seam and therefore close the neckline, which results in a serged seam exposed at the neck edge. This is usually stitched down with a few straight stitches across the width of the binding but my machine HATES doing this so it drives me crazy. This is avoided totally when binding in the round.
So...... as I was sewing in a sleep deprived state the other day, in my overly cramped sewing space where I have to keep changing my machines over between my standard machine and my serger, I was struck with a flash of brilliance (or something) so I thought I'd share. (For all those of you who already do your binding like this feel free to burst my brilliance bubble but why oh why haven't you told me about it!).
Here you go (note I used a cotton/lycra as my binding and it does curl slightly which shows in some of the photos, this doesn't happen with many other knit fabrics).
Step 1: Stitch one shoulder seam
Step 7: Now fold the binding over to the wrong side, covering the neck edge seam allowance and folding this towards the binding (so it is encased by the binding). Pin in place carefully putting pins on the right side of the garment.