As a little girl, I remember watching my Grandfather lay tefillin. I would stand at the door watching what he considered his personal time with God. I was always amazed with his devotion and care given to this time of the morning. The first thing he always did was to put on his tallis.
The tefillin was always kept in a velvet bag. I would watch as he first removed the shel yad from the bag. This would be placed on his arm near the biceps. The black box was placed right in the center of his arm. After doing this, the first prayer was said.
Once the prayer was completed, the strap was wound once around the arm, near the box and then brought down towards the hand. It was wrapped around his arm seven times as it headed towards his hand.
Next the shel rosh, the piece placed on the head, was taken out of his bag. The box was placed in the center of his forehead. The next prayer was then said. After finishing this prayer, the straps were tied into some form of a knot at the back of the head. He then said his third prayer of the morning.
Next, Grandfather would continue wrapping the rest of the strap around his wrist. Bringing the strap from the back of your hand, pull it under the middle finger. Bring it around the top of the finger and wrap it once around the top of the finger and than twice around the bottom half of the finger. This is done while saying the fourth prayer.
From this point, there are only a few additional steps one must take to properly complete the laying of tefillin. From the bottom of the middle finger, take the strap around the ring finger. From here the strap must come across the top of the hand and then across the palm. Keep wrapping it until the straps are almost done. Then tuck the end into the strap to keep it firm while you Daven.
The tefillin is removed by unstrapping the palm straps and doing everything backwards, ending with the top of your arm. Finally, the shel rosh is removed and placed back in the bag. This bag is usually placed in a drawer where it couldn't be touched by anyone else. Upon the believer's death, it will be placed in the coffin with him.
When my Grandfather was done with all of this, I remember him smiling at me and telling me to have a good day as he had prayed for me.