Machine the binding to the front, ensuring that when folded to the back, the binding will just cover the line of stitching. Load a sharp needle with a decent length of cotton. I always make it far too long, to minimise restarting, but that's a personal preference. Start by bringing the needle through the quilt sandwich at the point you want to start (not too close to a corner) right in the seam.
Fold the binding over and hold in place with your left hand (this all assumes you're right handed!). I rarely if ever pin.
Insert the very tip of the needle into the fold of the binding (the angle of the needle here is wrong, but I needed my hand to take the photo; it should be at about 15 degrees to the line of sewing).
Slide the needle along inside the fold about half a centimetre.
Still at the same angle, push the needle down through the bottom layer of the binding, straight into the backing, about half a centimetre from where you went into the binding. It should go into the backing directly underneath the fold. Although the position of the needle looks as though the finger on the hand holding the binding in place is guiding the needle, it's not. The left hand only holds the binding in place.
Ease the needle along under the backing but not into the batting, for another half centimetre, then, pushing down with your left thumb to bend the sandwich back a little, poke the needle back up through the backing, directly underneath the fold of the binding.
That's a full stitch - a bit in the binding and a bit in the backing. You load the two parts of the stitch onto the needle at the same time, then pull the thread through. Wherever the thread moves between the two layers, the entry and exit points of the needle should be on top of one another, so that once complete, the thread never travels along between the layers. this is what keeps it both firm and invisible.
Because of the insanely long threads I use, I find it easiest to do 5-10 of these at a time, just pulling about 15cm of thread through each, then pull the whole lot through after the last one. Experiment how easily you can pull the thread through multiple stitches before trying 10 at once.
Here's some completed binding photographed from the side, rather than above. From above the stitching is completely invisible. From the side, even with the high-contrast thread, once the stitches are pulled taut, you don't see the stitches, but you can see where the thread is in the binding, pulling it down to meet the quilt sandwich.
I usually get about 5 stitches in the gap between finger and thumnb before folding over the next bit of binding and replacing my hand.