For years this method has been my go-to method for finishing off the neck opening. However, don't use this on any boys' shirts. This is more a feminine look. For boys or men use ribbing on the neck. This binding method can also easily be used to finish off sleeve hems for a different look.
Here's how I do this, which is also the same method I use to do contrasting binding on a swimsuit, minus encasing elastic into the binding.
I start out w/ 2 inch wide strips of fabric.
I like to have plenty of fabric to work with.
Figure out the size of the neck opening and cut your binding strip at least 1-1/2 inches shorter than that measurement. I measure rather "accurately" by just folding the neck opening in half and laying out the binding piece and cutting it shorter as shown above. Do what makes you most comfortable.
I attach my binding to the shirt, right sides together, with a 3/8" seam.
Only stretch the binding just enough to fit it to the neck opening.
You do NOT want to stretch the shirt at all.
After sewing the binding onto the neck opening, trim away some of fabric to reduce the bulk.
I do this at the neck binding seam as well as cut away a bit of the fabric at each shoulder seam.
Once this is done you will flip the binding strip back over the seam allowance towards the inside of the shirt.
Pin in place, below.
Then use whichever method you prefer to topstitch the binding in place.
Options: twin needle
single needle topstitch
white for the binding side and then black for the shirt side.
Then all that is left is to cut away the remainder of the strip.
Be very careful when you do this to NOT cut the shirt.
I always try to angle my scissors, shown below, so that I am less likely to nick my shirt fabric.
Here is another option below using this method--very contrast binding with a little ruffle embellishment like a tuxedo and then the binding also on the sleeve hems.
One more shirt that we made using this method, but with a pleated strip encased into the neck binding. This strip was about 1-1/2 inches wide and we only pleated the front half of the shirt from shoulder seam to shoulder seam.
Clearly pleased with how it turned out.
The only drawback to this pleated style is that after every wash we are going to have to iron the pleats again.
It may only be the fabric that is the issue, but even still I'm not really into ironing, if I can help it.
However, she loves it, and so she can do the ironing.