Temari, coming from words hand (te) and ball (mari), truly began as a simple toy. Around 7th century game Kemari (similar to hacky sack nowadays) derived from China's Cuju game was introduced in Japan. At first, it was played with leather ball. But as the ball games evolved into tossing and catching, first hand balls were created. Those were made mostly from scraps of old kimonos, wrapped with string so tightly that they would actually bounce.
Around 16th century, noblewomen started wind the balls with colorful silk threads and embroidering them. While competing with one another, the patterns would become more and more perfected and intriguing. Mothers gave temari to they children on New Year's Eve, not just for playing, but as a "love token". Inside some mari cores you could even find piece of paper with mother's wish for child's well being. But that is not all there is inside, some where noise makers too. Sometimes tassels are added.
Thus a creation of simple toys slowly leaded to complex art objects.
Modern temari making
Nowadays some artists still makes their own mari cores from cloth strips and wool, but usually you would see ones started with styrofoam, wooden or soft tennis ball. Those are carefully covered in few layers of threads. Starting with wool or other stronger thread base layer for easier embroidering is created, followed with thinner threads. Last one is sewing thread, which makes the surface as much smooth as possible. In this whole process, maker has to keep finely winding all the time, trying to achieve a perfect sphere, resulting in time consuming preparatory step. If the ball is too off, the pattern would show the mistake quite heavily.
After core is made, you have to measure up base lines for pattern of your choice. This is made with just paper strips, pins and marking threads. The classical patterns have simple or combination divisions, for mostly symmetrical and geometric designs, but there are some freely stitched designs as well.
Simple division is one where there are two faces or centers, it is compared to Earth's two poles with number of meridian lines linking them. Meridians then divide the ball usually into quarters, eights, twelfths or other even number. The "equator" line is measured too, splitting the mari into two hemispheres. Patterns are usually centered around the poles, traditionally making flowers or stars, but there are also belt designs (=Obi patterns) for equator.
Combination division just have more faces. They are little harder for measuring and more demanding when it comes to perfect winded maris. Most combination patterns needs 4, 6, 8 or 10 faces, but you could find a multicentred ones, with more then 100 centers.
When marking is done, you can finally start stitching or wrapping, using colorful embroidery threads. The stitches are in fact very easy and a few, but there is almost no limit to designs, as you can always change any pattern to your own liking and imagination. Used colors and numbers (for example number of petals of kiku, a chrysanthemum design) can have their own meaning. Finished pieces are still given to family or friends as a meaningful gift, as temari represents wishes for happiness.
Whole mari covering design:
If you are interested in trying temari, there are various sites with step by step photo tutorials and patterns, best one being TemariKai. There is also #Temari-Creations group here on DA.