Step 1:  Thread a needle with approximately 24 inches of thread.  Take both ends of the thread and knot it so that you have a tail after the knot approximately 1 1/2 inches long.  Don't cut off the tail.

Step 2:  Push the needle from the back of the fabric to the front of the fabric where you want the button to be, stopping at the knot you created in step 1.  Don't tug too hard.

Please note that the images below show  a single threaded needle and does not show the fabric.
 

Step 3:  Slip the button onto the needle.
Step 4:  Pull the needle out of the fabric with the button resting on the fabric.
Step 5:  Push the needle through the next hole back into the fabric.
Step 6:  Pull the needle until the button is resting flat against the fabric.
Step 7:  Push the needle through the next hole.
Step 8:  Push the needle back into the fabric through the last hole.
Step 9:  Pull the needle until the button is resting flat against the fabric.
Step 10:  Push the needle through the first hole we started on.
Step 11:  Push the needle back into the fabric.
Step 12:  Push the needle through the hole.
Step 13:  Push the needle through the hole to the back of the fabric.  Your button is now sewn to your fabric.
Step 14:  You will need to tie off your thread or your button will "pop" right off.  Use the "tail" and the thread on the needle to tie a square knot on the back of your fabric.  Pull the needle off the thread and place in a pincushion.  Follow the steps to tie a square knot: LEFT (yellow) over RIGHT (red).
Step 15:  Pull tight until the knot sits on the fabric -- this is called an "overhand knot".
Step 16:  Then, RIGHT (red) over LEFT (yellow) and pull tight -- this is called a "square knot". Clip the threads close to the knot, but DON'T cut off the knot!