Thread your needle and measure where your button needs to go
Make a knot in your thread about 1cm from the end of the thread (see the video on a foolproof way to do this)
Make a couple of anchor stitches where you will be sewing on the button
Thread the needle through one of the holes in the button and push the button down the thread until it is sitting in the right place on your garment.
Making sure to line up the holes on the button in the same direction that all the other buttons holes are lined up, push the needle down through the 2nd hole in the button and push through to the back of the fabric.
Take the needle up through the fabric and the 1st hole in the button. Continue to sew the button on in the manner until you have gone in and out of both holes in the button about 10 times, finishing with your needle and thread at the top of your garment.
Take the needle and thread through the 1st hole in the button, but not through the fabric, and pull through so that the needle and thread come out between the button and the fabric.
Wind the thread around the button about 5 times. This will strengthen the sewing and make the button more stable.
Take the needle and thread back through the fabric to the back of the garment and make a few small anchor stitches.
Make a knot in the thread right at the base, closes to the fabric (see the video on a foolproof way to do this,
Push the needle and thread through between the layers of fabric and cut off the thread so that the end of the thread is between the layers of fabric.
Turn to the right side and snip off the end of the thread, which is between the button and the fabric, but not too close to the knot so that the knot does not unravel. The rest of the loose thread will be between the button and the fabric so it won't be seen.